· 6 years ago · Jan 21, 2020, 12:02 PM
1UNIT-I SETS AND LOGIC
2
3ONE MARKS QUESTION
41. An if-then assertion whose first clause is true is
5A. never true;
6B. sometimes true;
7C. always true;
8D. meaningless;
9ANSWER: B
10
112. A rigorous demonstration of the validity of a theorem or assertion is called a(n)
12A. proof;
13B. deduction;
14C. contradiction;
15D. induction
16ANSWER: A
17
18
193. ^ denotes
20A. set membership;
21B. union;
22C. AND;
23D. a relation between sets;
24E. negation
25ANSWER: C
26
274. ¬ denotes
28A. set membership;
29B. union;
30C. AND;
31D. a relation between sets;
32E. logical negation
33ANSWER: E
34
355. Logic manipulates
36A. numbers;
37B. algorithms;
38C. truth values;
39D. sound;
40E. strings
41ANSWER: C
42
436. v denotes
44A. set membership;
45B. union;
46C. AND;
47D. OR;
48E. implication
49ANSWER: D
50
517. => denotes
52A. set membership;
53B. union;
54C. AND;
55D. OR;
56E. implication
57ANSWER: E
58
598. A proof that begins by asserting a claim and proceeds to show that the claim cannot be true is by
60A. induction;
61B. construction;
62C. contradiction;
63D. prevarication;
64ANSWER: C
65
669. Proofs by contradiction
67A. dismiss certain rules of logic;
68B. misrepresent facts;
69C. start by assuming the opposite of what is to be proven;
70D. end by rejecting what is to be proven;
71ANSWER: C
72
7310. Induction is a(n)
74A. algorithm;
75B. program;
76C. proof;
77D. proof method;
78ANSWER: D
79
8011. The induction principle makes assertions about
81A. infinite sets;
82B. large finite sets;
83C. small finite sets;
84D. logical formulas;
85E. programs
86ANSWER: A
87
8812. In an inductive proof, showing that P(0) is true is
89A. the base step;
90B. the inductive step;
91C. sufficient to prove P(x + 1);
92D. sufficient to prove P(x) for all x
93ANSWER: A
94
9513. In an inductive proof, showing that P(x) implies P(x + 1) is
96A. the base step;
97B. the inductive step;
98C. sufficient to prove P(x) for some x;
99D. sufficient to prove P(x) for all x
100ANSWER: B
101
10214. The base step in an inductive proof might
103A. show that P(0) is true, and that P(x) implies P(x + 1);
104B. show that P(0) is true;
105C. show that that P(x) implies P(x + 1);
106D. assume the opposite of what is to be proven
107ANSWER: B
108
10915. The inductive step in an inductive proof might
110A. show that P(0) is true, and that P(x) implies P(x + 1);
111B. show that P(0) is true;
112C. show that that P(x) implies P(x + 1);
113D. assume the opposite of what is to be proven
114ANSWER: C
115
11616. An entire inductive proof might
117A. show that P(0) is true, and that P(x) implies P(x + 1);
118B. show that P(0) is true;
119C. show that that P(x) implies P(x + 1);
120D. assume the opposite of what is to be proven
121ANSWER: A
122
12317. Which of the following statement is the negation of the statement , “2 is even and –3 is negative”?
124A. 2 is even and –3 is not negative.
125B. 2 is odd and –3 is not negative.
126C. 2 is even or –3 is not negative.
127D. 2 is odd or –3 is not negative.
128ANSWER: D
129
13018. ∩ denotes
131A. set membership
132B. intersection
133C. conjunction
134D. negation
135ANSWER: B
136
13719. Ø denotes
138A. set membership
139B. union
140C. AND
141D. empty set;
142E. negation
143ANSWER: D
144
14520. € denotes
146A. set membership
147B. union
148C. AND
149D. a set
150E. negation
151ANSWER: A
152
15321. A string is a
154A. collection
155B. set
156C. tree
157D. sequence;
158E. list
159ANSWER: B
160
16122. {1,2,3} U {2,4,5} =
162A. {}
163B. {1,2,3,2,4,5}
164C. {2}
165D. {1,2,3,4,5}
166ANSWER: D
167
16823. {1,2,3} ∩ {2,4,5} =
169A. {}
170B. 2
171C. {2}
172D. {1,2,3,4,5}
173ANSWER:C
174
17524. {} is a subset of
176A. itself only
177B. no set
178C. all sets;
179D. only infinite sets
180ANSWER: C
181
18225. p→q is logically equivalent to
183A. ~ q →p
184B. ~ p→q
185C. ~ p v q
186D. ~ p ^ q
187ANSWER: D
188
18926. If P and Q stands for the statement P : It is hot Q : It is humid, then what does the following mean? P ~ Q:
190A. “It is hot and it is not humid”.
191B. “ it is hot and humid”
192C. “ It is hot or it is not humid”
193D. “ It is hot or humid”
194ANSWER: A
195
19627. Which of the following set is null set?
197A. 0
198B.
199C.
200D. {NULL}
201ANSWER: B
202
20328. Let A be a finite set of size n. The number of elements in the power set of A is:
204A. 22n
205B. 2n
206C. 2n
207D. n+1
208ANSWER: B
209
21029. Let p be “He is tall” and let q “He is handsome”. Then the statement “It is false that he is short or handsome” is:
211A. p q
212B. ~ ~ p q
213C. p~ q
214D. ~ p q
215ANSWER: B
216
21730.Let P(S) denotes the powerset of set S. Which of the following is always true?
218A. P(P(S)) P(S)
219B. P(S) ∩ S P(S)
220C. P(S) ∩ P(P(S))
221D. SP(S)
222ANSWER: D
223
22431. What is the converse of the following assertion. I stay only if you go.
225A. I stay if you go.
226B. If you do not go then I do not stay
227C. If I stay then you go.
228D. If you do not stay then you go.
229ANSWER: B
230
23132. Which one is the contrapositive of q p ?
232A. p q
233B. ¬p ¬q
234C. ¬q ¬p
235D. None of these
236ANSWER: B
237
23833. What is the representation of the following statements into predicate calculus forms “Not all birds can fly.” Assume bird(x): “x is bird” fly(x): “x can fly”.
239∃x bird(x) ~ fly(x)
240B. ∃x bird(x) v ~ fly(x)
241C. ∀x bird(x) ~ fly(x)
242D. ∀x bird(x) v ~ fly(x)
243ANSWER: A
244
24533. What is the representation of the following statements into predicate calculus forms “ There is a student who likes mathematics but not history.” Assume student(x): “x is student.” likes(x, y): “x likes y”.
246A.x [student(x) vlikes(x, mathematics) ~ likes(x, history)]
247x [student(x) likes(x, mathematics) ~ likes(x, history)]
248C. x [student(x) likes(x, mathematics) likes(x, history)]
249D.x [student(x) likes(x, mathematics) ~ likes(x, history)]
250ANSWER: B
251
25234. What is the negation of the statement xyxy 1
253x [~y (xy = 1)]
254x y [~(xy = 1)]
255Cx y (xy 1)
256D.x y (xy 1)
257ANSWER: C
258
25935. Write the negation of each of the following in good English sentence.“I will not win the game or I will not enter the contest.”
260A. I will win the game and I will enter the contest.
261B. I will win the game or I will enter the contest.
262C. I will win the game and I will not enter the contest.
263D. I will not win the game and I will enter the contest.
264ANSWER: A
265
26636. Let A and B be mutisets, A={1,1,1,2,2,3} and B={1,1,4,3,3} then AUB is
267A. {1,1,2,2,3,3,4}
268B. {1,1,1,2,2,3,3,4}
269C. {1,1,1,2,2,2,3,3,4}
270D. {1,1,3}
271ANSWER: B
272
27337. If p,q,and r are the set of premises then which is the law given. ((p q) pq is a tautology
274A. Modus Tollens
275B. Modus Ponens
276C. Hypothetical Syllogism
277D. Disjunctive Syllogism
278ANSWER: B
279
28038. A validity-maintaining procedure for deriving sentences in logic from other sentences is a(n) A. proof;
281B. theorem;
282C. algorithm;
283D. inference rule;
284E. inference chain
285ANSWER: D
286
28739.. p iff q means
288A. p q q p;
289B. p q q p;
290C. p q but not necessarily q p;
291D. q p but not necessarily p q;
292ANSWER: A
293
29440. The property asserted by (p q q r) (p r) is
295A. commutative;
296B. transitive;
297C. undecidable;
298D. time dependent;
299E. associative
300ANSWER: B
301
30241. The property asserted by (p = q q = r) (p = r) is
303A. commutative;
304B. transitive;
305C. undecidable;
306D. time dependent;
307E. associative
308ANSWER: A
309
31042. (p q) iff
311A. p q;
312B. p q;
313C. p q;
314D. p q;
315E. q p
316ANSWER: E
317
31843. Inference rules maintain
319A. completeness;
320B. consistency;
321C. validity;
322D. satisfiability;
323E. falsehood
324ANSWER:C
325
326
327 44. Following are two sentences. A:2+3=5 B: Read this carefully Which of the following os correct?
328A. A and B both are proposition
329B. A is proposition but B is not.
330C. B is proposition but A is not.
331D. Both A and B are not proposition.
332ANSWER: B
333
33445. Negation of the proposition”Today is Friday”
335A. Today is Saturday
336B. Today is not Friday
337C. Yesterday was Friday
338D. Tommorrow will be Friday
339ANSWER: B
340
34146. Truth value of p is true and q is false, then which of the following has truth value false.
342A. p q
343B. p v q
344C. p ~ q
345D. q p
346ANSWER: A
347
34847. p q is equivalent to
349A. (p q) v (q p)
350B. (~p q) (q~ p)
351C. (p q) (p ~q)
352D. (p q) (q p)
353ANSWER: D
354
35548. p: Today is Sunday q: Today is holiday contrapositive of “ Today is Sunday hence it is holiday is”
356A. If today is not holiday then it is not Sunday
357B. If today is not Sunday then it is not holiday
358C. If today is holiday then it is Sunday
359D. Today is Sunday hence it is holiday.
360ANSWER: A
361
36249. Truth value of “ if 2+2=4 then x+1=1 “ is true when
363A. x=0
364B. x=1
365C. for any integer value of x
366D. for any real value of x
367ANSWER: A
368
36950. “ You can access the internet from campus only if you are a computer science student and you are not freshman” P: You can access the internate Q: You are computer science student R: You are freshman
370A. Q v ~ RP
371B. Q v RP
372C. ~(Q vR) P
373D. (Q ~ R) P
374ANSWER: D
375
37651. The converse of p q is
377A. q p
378B. ~p ~q
379C. ~ q~ p
380D. ~( p q)
381ANSWER: A
382
38352. The inverse of p q is
384A. q p
385B. ~p ~q
386C. ~ q~ p
387D. ~( p q)
388ANSWER: B
389
390
39153. The contrapositive of p q is
392A. q p
393B. ~p ~q
394C. ~ q~ p
395D. ~( p q)
396ANSWER: C
397
39854. The negation of p q is
399A. q p
400B. ~p ~q
401C. ~ q~ p
402D. ~( p q)
403ANSWER: D
404
40555. P is equivalent to
406A. P v T
407B. P
408C. T
409D. ~ P
410ANSWER: B
411
41256. P v T is equivalent to
413A. P T
414B. P
415C. T
416D. ~ P
417ANSWER: C
418
41957. A: P T≡P B: P v≡ T C: P vF ≡ P D: P F ≡ F . Which of the following is correct?
420A. A and C are correct only
421B. Only B and D are correct.
422C. all are wrong
423D. All A,B,C and D are correct.
424ANSWER: D
425
426
427
428
429
430
431
432
433TWO MARKS QUESTION
434
43558. If p = false, q = false, and r = true, then which is not true?
436A. ¬p ^ (q ^ r);
437B. ¬p v (q ^ r);
438C. (¬p v q) ^ r;
439D. p v ¬ (q ^ r)
440ANSWER: A
441
442P Q~ P Qis a
443A. contradiction
444B. contingency
445C. tautology
446D. satisfiable
447ANSWER: A
448
44960. The description of the shaded region in the following figure using the operations on set is,
450
451
452A. CA B
453B. C A CCBA B
454C. C A CCBA B
455D. A BC CA B
456ANSWER: B
457
45861. The statement ( pq) → p is a
459A. Contingency.
460B. Absurdity
461C. Tautology
462D. Contradiction
463ANSWER: C
464
46562. Which of the following proposition is a tautology?
466A. (p v q)p
467B. p v (qp)
468C. p v (pq)
469D. p(pq)
470ANSWER: C
471
47263. What is DNF form of the following:
473(p q) (~ pq)
474A. (~ p v q) (~ pq)
475B. (~ p q) v(~ pq)
476C. (~ p ~ p q) v(q ~ pq)
477D. pq
478ANSWER: B
479
48064. If A and B are two subsets of a universal set then A-B IS equivalent to
481A. A
482B. B – A
483C. A U
484D. A
485ANSWER: A
486
48765. In a class of 60 boys, 45 boys play cards and 30 boys play carrom. How many boys play
488both games?
489A. 25
490B. 30
491C. 15
492D. 45
493ANSWER: C
494
49566. (AUB)∩(AUBC ) is equal to
496A. A
497B. Ø
498C. A ∩ BC
499D. Universal set
500ANSWER: A
501
50267. The statement ~ ( pq) v (p x q) is a, where x is a biconditional
503A. Contingency.
504B. Absurdity
505C. Tautology
506D. Contradiction
507ANSWER: C
508
50968. The statement ( ~p→r) p x q) is a, where x is a biconditional
510A. Contingency.
511B. Absurdity
512C. Tautology
513D. Contradiction
514ANSWER: A
515
51669. The Proposition is P p vq) is
517A. Absurdity.
518B. Logically equivalent to pq
519C. Tautology
520D. Contradiction
521ANSWER: B
522
52370.Which of the following is a tautology
524A. a v b b c
525B. a b b c
526C. a v b (b c)
527D. a b bc)
528ANSWER: B
529
53071. (P V Q) (P R) (Q S) is equivalent to
531A. S R
532B. S v R
533C. S R
534D. S < R
535ANSWER: C
536
53772. (p q) (r q) is equivalent to
538A. (p v r)q
539B.p v (r p)
540C. p v (r q)
541D. p (q r)
542ANSWER: A
543
54473. The statement ~( p vq) → q is a
545A. Contingency.
546B. Absurdity
547C. Tautology
548D. Contradiction
549ANSWER: A
550
551
55274. The statement p→( q →p) is a,
553A. Contingency.
554B. Absurdity
555C. Tautology
556D. Contradiction
557ANSWER: C
558
55975. The statement (p q) p v q) is
560A. Contingency.
561B. Absurdity
562C. Tautology
563D. Contradiction
564ANSWER: D
565
56676. The statement ( p→ q) q v ~ p)) is a,
567A. Contingency.
568B. Absurdity
569C. Tautology
570D. Contradiction
571ANSWER: C
572
57377. The statement (p ( ~p v q)) q is a,
574A. Contingency.
575B. Absurdity
576C. Tautology
577D. Contradiction
578ANSWER: D
579
580
581
582FOUR MARKS QUESTION
583
58478. In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea. Also 13 like both milk and tea, 15 like milk and coffee, 20 like tea and coffee and 12 like none of the three drinks. Find the number of people who like all the three drinks.
585A. 73
586B. 8
587C.72
588D. 10
589ANSWER: B
590
59179. Determine the number of integers between 1 and 250 that are divisible by any of the integers 2, 3, 5 and 7.
592A. 1
593B. 193
594C. 125
595D. 8
596ANSWER: B
597
59880. [ p q~ rq Is the given proposition is?
599A. Contingency.
600B. Absurdity
601C. Tautology
602D. Contradiction
603ANSWER: A
604
60581. In a group of athletic teams in a certain institute, 21 are in the basket ball team, 26 in the hockey team, 29 in the foot ball team. If 14 play hockey and basketball, 12 play foot ball and basket ball, 15 play hockey and foot ball, 8 play all the three games. (i) How many players are there in all? (ii) How many play only foot ball?
606A. 43, 10
607B. 10, 43
608C. 10, 45
609D. 45, 10
610ANSWER: A
611
61282. A survey of 500 television watchers produced the following information, 285 watch football games, 195 watch hockey games, 115 watch basketball games, 45 watch football and basketball games, 70 watch football and hockey games, 50 watch hockey and basketball games and 50 do not watch any of the three kinds of games. a) How many people in the survey watch all three kinds of games? b) How many people watch exactly one of the sports?
613A. 20, 324
614B. 30, 325
615C. 20, 325
616D. 21, 330
617ANSWER: C
618
61983. A local Merchant uses television, radio and newspaper advertising. To determine the effectiveness of advertising, he questions 200 customers during a special after hours sale to see, how many knew about sale. He found that 115 had been television ads, 75 had heard radio ads, and 125 had heard newspaper ads. He also found that 30 received information from television and radio, 70 from television and newspapers, 25 from radio and newspapers and 10 from all three. If everyone else said they heard it from a friend. How many heard it from a friend?
620A. 105
621B. 100
622C. 95
623D. 90
624ANSWER: C
625
62684. In a survey of 85 people it is found that 31 like to drink milk 43 like coffee and 39 like tea.
627Also 13 like both milk and tea, 15 like milk and coffee, 20 like tea and coffee and 12 like
628none of the three drinks. Find the number of people who like all the three drinks.
629A. 48
630B. 23
631C. 8
632D. 12
633ANSWER: C
634
63585. The statement ( (~pq) v ( q r))→r is a
636A. Contingency.
637B. Absurdity
638C. Tautology
639D. Contradiction
640ANSWER: A
641
642Unit-1(Sets & proposition)
643Q. 1 Let p (s) denote the power set of set S. Which of the following is always true
644(a) p (p (s)) = p (s)
645(b) p (s) ∩ s = p (s)
646(c) p (s) ∩ p (p (s) = { φ }
647(d) s ∉ p (s) Ans. : (c)
648Q. 2 Let A and B be sets and A C and B C denote the complements of
649the set A and B. The set (A – B) ∪ (B – A) ∪ (A ∩ B) is equal to
650(a) A ∪ B
651(b)A C ∪ B C
652(c) A ∩ B
653(d)A C ∩ B C Ans. : (a)
654Q. 3 The number of elements in the power set p (s) of the set
655S = { { φ }, 1, {2, 3}} is
656(a) 2
657(b) 4
658(c)8
659(d) None Ans. : (c)
660Q. 4 Let S be an infinite set and S 1 , S 2 , S 3 .........S n be sets such that
661S 1 ∪ S 2 ∪ S 3 ∪ ..............S n = S. Then
662(a) At least one of the set S i is a finite set.
663(b) Not more than one of the set S i can be finite.
664(c) At least one of the set S i is an infinite set
665(d) None of these . Ans. : (c)
666Q. 5 Let A be a finite set of size n, the number of elements in the power set of A × A
667is,
668(a) 2 2n
669(b) 2 n2
670(c)(2 n ) 2
671(d) None of these Ans. : (b)
672Q. 6 The power set 2 s of the set S = {3, {1, 4}, 5} is,
673(a) {S, 3, 1, 4, {1, 3, 5 }, {1 4, 5}, {3, 4}, φ }
674(b) {S, 3, {1, 4}, 5}
675(c) {S, {3}, {3, {1, 4}, {3, 5}, φ }
676(d) None of these Ans. : (d)
677Q. 7 Consider the following statements
678S 1 There exist infinite set A, B and C such that A ∩ (B ∪ C) in finite
679Unit-1(Sets & proposition)
680S 2 : There exist two irrational number x and y such that (x + y) is rational.
681(a) Only S 1 is correct
682(b) Only S 2 is correct
683(c) Both S 1 and S 2 are correct
684(d) None of S 1 and S 2 is correct
685Ans. : (c)
686Q. 8 In a room containing 28 females, there are 18 females who speak English, 15 female
687speak French and 22 speaks German. 9 female speak both English and French, 11
688females speak both French and German whereas 13 speak both German and English.
689How many females speaks all the three language ?
690(a) 9
691(b) 8
692(c) 7
693(d) 6 Ans. : (d)
694Q. 9 The number of substring of all lengths that can be formed from a character
695string of length n = ?
696(a) n
697(b) n 2
698(c) n (n – 1)/2
699(d) n (n + 1)/ 2 Ans. : (d)
700Q. 10 ............ is an unordered collection of elements where an element can occur
701as a member more than once.
702(a) Multi set
703(b)Ordered set
704(c) Set
705(d)None of these Ans. : (a)
706Q. 11 Which of the following sets are equal ?
707A = {x : x 2 – 4x + 3 = 0}, B = {x : x 2 – 3x + 2 = 0} C = {x : x ∈ N, x < 3}, D = {x : x
708∈ N, x is odd, x < 5} E = {1, 2}, F = {1, 2, 1}, G = {3, 1}, H = {1, 1, 3}
709(a) A and B
710(b) C and E
711(c) F and H
712(d) B and D Ans. : (b)
713Q. 12 The set which is superset of all the set under consideration at a moment of
714time are called
715(a) Set of set
716(b)Universal set
717(c) Union of set
718(d)Infinite set Ans. : (b)
719Q. 13 If A ⊆ B then B is called
720(a) Subset of A
721(b)Superset of A
722(c) Singleton set
723(d) Empty set Ans. : (b)
724Q. 14 If each element of A is also an element of B and set B has at least one
725element which is not an element of set A. Then A is called
726(a) Proper subset
727(b) Superset
728(c) Universal set
729(d) None of these Ans. : (a)
730Q. 15 If A = {a, e, i, o, u} and B = {1, 3, 5, 7, 9}
731Then A and B are called
732(a) Equivalent set
733(b) Equal set
734(c) Power set
735(d)Subset Ans. : (a)
736Q. 16 If A = {a, b, c, p, q, r} and B = {p, q, r, a, b, c}
737Then A and B are called
738(a) Equal set
739(b)Equivalent set
740(c) Universal set
741(d) Subset Ans. : (a)
742Q. 17 Cardinality of set gives the
743(a) Exact elements of that set
744(b) Exact number of elements present in that set
745(c) Union of the set
746(d) Intersection of the set Ans. : (b)
747Q. 18 If set A is having n number of elements then powerset of A is,
748(a) n 2
749(b) 2
750(c)2 n
751(d) n/2 Ans. : (c)
752Q. 19 If A = {a, b, c, d, e}
753B = {1, 2, 3, 4, 5}
754A ∪ B = ?
755(a) {a, b, c, d, e, 1, 2, 3}
756(b) {1, 2, 3, a, b, c, 4, 5, d, e}
757(c) {a, b, c, d, e}
758(d) {1, 2, 3, 4, 5} Ans. : (b)
759Q. 20 Considering Question 19, what is A ∩ B
760(a) { φ }
761(b) {a, b, c, d, e}
762(c) {1, 2, 3, 4, 5}
763(d) None of the above Ans. : (a) 3
764Q. 21 If A = {a, b, c, p, q,r}
765B = {1, 2, 3, p, q, r}
766Find A – B
767(a) {a, b, c}
768(b){1, 2, 3}
769(c) {1, 2, 3, p, q, r}
770(d) None of the above Ans. : (a)
771Q. 22 Considering Question 21, find A ⊕ B.
772(a) {a, b, c, 1, 2, 3,}
773(b) {a, b, c}
774(c) {1, 2, 3}
775(d)None of the above Ans. : (a)
776Q. 23 What is the notation for given Venn diagram ?
777(a) A ∪ B
778(b)A ∩ B
779(c) A ⊆ B
780(d) A ⊕ B Ans. : ©
781Q. 24 Which one is the notation for Venn diagram ?
782(a) A ∪ B
783(b) A ∩ B
784(c) A ⊕ B
785(d) A ⊆ B Ans. : (c)
786Q. 25 Which one is the correct notation for the given
787diagram ?
788(a) A ∪ B
789(b) A – B
790(c) A ⊕ B
791(d) A ⊂ B Ans. : (b)
792Q. 26 Which is correct notation for the given Venn diagram ?
793(a) A ∩ B = φ
794(b) A ∪ B = φ
795(c) A ⊆ B
796(d) None of these Ans. : (a)
797Q. 27 If A = {{a, b}, {1}, {1, 2, 3, 4} } A is called
798(a) Set of sets
799(b)Superset
800(c) Multiset
801(d)Union of set Ans. : (a)
802Q. 28 Let A = {1, {1, 2} }
803The p (A) contains how many elements ?
804(a) 8
805(b) 4
806(c)6
807(d) None of these Ans. : (b)
808Q. 29 Which of the following is true
809(a) p ∧ Q is true when both p and Q are true
810(b) p ∧ Q is true when any one p and Q is true
811(c) p ∧ Q is true when both p and Q are false Ans. : (a)
812Q. 30 p → Q is false when
813(a) both p and Q are true
814(b) both p and Q are false
815(c) p is true and Q is false
816(d) p is false and Q is true Ans. : (c)
817Q. 31 Which of the following are true ?
818(a) (p ∨ ∼ p) and (p ∧ ∼ p) both are tautology
819(b) (p ∨ ∼ p) and (p ∧ ∼ p) both are contradiction
820(c) (p ∨ ∼ p) is a tautology and (p ∧ ∼ p) is a contradiction
821(d) (p ∨ ∼ p) is a contradiction and (p ∧ ∼ p) is a tautology. Ans. : (c)
822Q. 32 p ⊕ Q is true when
823(a) Both p and Q are true
824(b) Both p and Q have some truth value
825(c) Both p and Q are false
826(d) Both p and Q have different truth value Ans. : (d)
827Q. 33 If p ↑ Q is false then
828(a) p is T and Q is F
829(b) p is F and Q is T
830(c) p is T and Q is T
831(d) p is F and Q is F Ans. : (d)
8325
833Q. 34 p ↓ Q is true when
834(a) p is T and Q is F
835(b) p is F and Q is T.
836(c) p is T and Q is T
837(d) p is F and Q is F Ans. : (d)
838Q. 35 A formula or statement having n propositional variable is
839p (p 1 , p 2 , p 3 , K, p n ) has
840(a) 2 n rows in truth table
841(b) 2 n rows in truth table
842(c) n! rows in truth table
843(d) 2 rows in truth table Ans. : (b)
844Q. 36 Let T be a theorem which is true then converse of the theorem is,
845(a) Necessarily true
846(b) Not necessarily true
847(c) Necessarily false
848(d) None of these Ans. : (b)
849Q. 37 “There will be flood. If it is raining for long, then there will be flood” What can
850you conclude from the statement.
851(a) ∃ fallacy
852(b) There will be flood
853(c) It is raining for long
854(d) None of these Ans. : (a)
855Q. 38 “If I am o.k. then I will go to your place. I am not o.k.” What you conclude from
856the above statement ?
857(a) I will not go to your place
858(b) I will go to your place
859(c) ∃ fallacy of affirming the consequences
860(d) None of these Ans. : (d)
861Q. 39 Identify which one is not a statement.
862(i) She is a girl (ii) What is your name ? (iii) 7 + x = 100 (iv) 7 < 0 (v) Do this work. Which of
863these are not statement.
864(a) (IV, V)
865(b)(II, III)
866(c) (II, III, IV)
867(d) (II, III, V) Ans. : (d)
868Q. 40 What is the negation of “14 is even or 15 is odd” ?
869(a) 14 is odd or 15 is even
870(b) 14 is odd and 15 is even
871(c) 14 is even and 15 is odd
872(d) 15 is even or 14 is odd Ans. : (b)
873Q. 41 Which of the following is equivalent to [ (p ∧ Q) ∨ ( ∼ p ∧ ∼ Q)] ?
874(a) p → Q
875(b) Q → p
876(c) p ↔ Q
877(d) p Ans. : (c)
878Q. 42 Give the contra-positive of the following sentence.
879“If I am feeling well then you come”.
880(a) If you come then I am feeling well.
881(b) If I am not feeling well then you don’t come.
882(c) If you come then I am not feeling well.
883(d) If you don’t come then I am not feeling well. Ans. : (d)
884Q. 43 The formula p ∨ ( ∼ p ∧ Q) is,
885(a) Tautology
886(b) Contradiction
887(c) Satisfiable but not valid
888(d) Insatisfiable and invalid Ans. : (c)
889Q. 44 Consider the following symbols.
890p : Tom goes to Pune Q : Tom goes to Mumbai R : Tom goes to
891Patna What is the symbolic form of the following statement ? “It is
892not true that Tom goes to Pune or Mumbai but not Patna”.
893(a) ∼ (p ∨ Q) ∨ ∼ R
894(b) ∼ [(p ∨ Q) ∧ ∼ R ]
895(c) ∼ [(p ∨ Q) ∨ ∼ R]
896(d) ∼ [(p ∨ Q) ∧ R] Ans. : (b)
897Q. 45 Find the value of [ ∼ (p ∨ Q) ∧ ( ∼ p ∧ Q)]
898(a) T
899(b) F
900(c)p
901(d) Q Ans. : (b)
902Q. 46 p → p is,
903(a) Tautology (b)Contradiction (c) Contingency (d) None of these Ans. : (a)
904Q. 47 Consider the following symbol
905p : She likes mathematics Q : She likes physics R : She likes history What is the
906symbolic form of the following statement? “She likes mathematics and physics, or
907she does not like mathematics and history”.
908(a) (p ∧ Q) ∨ ∼ (p ∧ R)
909(b) (p ∧ Q) ∨ ( ∼ p ∧ ∼ R)
910(c) (p ∨ Q) ∧ ∼ (p ∨ R)
911(d) (p ∧ Q) ∨ ∼ (p ∨ R) Ans. : (a)
912Q. 48 The formula (p → Q) ↔ (Q → R) is,
913(a) Contradiction
914(b) Tautology
915(c) Satisfiable but not valid
916(d) Satisfiable and valid Ans. : (c)
917Q. 49 Which of the following pair is not equivalent.
918(a) [(A → B), {A → B}]
919(b) [(A ↔ B), {A ↔ (A ↔ B)}]
920(c) [B, {A ↔ (A ↔ B)}]
921(d) None of these Ans. : (b)
922Q. 50 Which of the following are equivalent
923(a) p ∨ (p ∧ Q), p ∧ (p ∨ Q)
924(b) p ∨ (p ∧ Q), p ∧ (p ∧ Q)
925(c) p ∨ (p ∧ Q), p ∨ (p ∨ Q)
926(d) None of these Ans. : (a)
927Q. 51 p → (Q → R) is equivalent to
928(a) (p ∧ Q) → R
929(b)(p ∨ Q) → R
930(c) (p ↔ Q) → R
931(d) None of these Ans. : (a)
932Q. 52 Among { ∼ (p → Q) → p} and {p ∧ (p ↔ Q)} → Q
933(a) One is tautology and other is contradiction
934(b) Both are tautology
935(c) Both are contradiction
936(d) One is satisfiable and other is unsatisfiable Ans. : (a)
937Q. 53 p : He exercise regularly
938Q : He is fit.
939R : He wants to become an athlete.
940Write the following statement in symbolic form “Exercise regularly is sufficient
941to be fit”.
942(a) Q → p
943(b)p → Q
944(c) p ↔ Q
945(d) None of these Ans. : (b)
946Q. 54 The value of p → {(Q ∧ R) → z } is
947(a) (p ∧ Q ∧ R) → z
948(b) (p ∨ Q ∨ R) → z
949(c) (p ∧ Q ∨ R) → z
950(d) (p ∨ Q ∧ R) → z Ans. : (a)
951Q. 55 The formula [{(p ∧ Q) → R} → {(R ∧ S) ↔ p}] → [p → (Q ∨ p)]
952(a) Tautology
953(b) Contradiction
954(c) Satisfiable
955(d)Not satisfiable Ans. : (a)
956Q. 56 The Transitive rule is,
957(a) Invalid rule of inference
958(b) Valid rule of inference
959(c) Satisfiable rule
960(d) None of these Ans. : (b)
961Q. 57 Which of the following is equivalent to (p ∨ Q) ?
962(a) (p ↑ Q) ↑ (p ↑ Q)
963(b) (p ↓ Q) ↓ (p ↓ Q)
964(c) (p ↑ Q) ↓ (p ↑ Q)
965(d) (p ↓ Q) ↑ (p ↓ Q) Ans. : (b)
966Q. 58 Which one of the following is equivalent to (p ∧ Q) ?
967(a) (p ↑ Q) ↑ (p ↑ Q)
968(b) (p ↑ p) ↑ (Q ↑ Q)
969(c) (p ↓ p) ↓ (Q ↓ Q)
970(d) (p ↑ p) ↓ (Q ↑ Q) Ans. : (c)
971Q. 59 If the proportion p → Q is true then the truth value of
972(p ∧ ∼ Q) → ((p ∧ Q) → p) is
973(a) True
974(b)False
975(c) Multiple valued
976(d) Can’t be determined Ans. : (a)
977Q. 60 The logical consequence of the formula
978(p → Q) ↔ (Q → R) ↔ (R → p) is,
979(a) p
980(b) Q
981(c) R
982(d) p ↔ Q Ans. : (d)
983Q. 61 Which of the following are valid
984(i) p → (p ∨ q) (ii) ∼ p → (p ∧ Q) (iii) (p ∧ (p → q)) → q (iv) (p → q) → (p ∨ Q)
985(a) I only
986(b) I and II
987(c) III and IV
988(d) I and III Ans. : (d)
989Q. 62 p ∨ (p → Q) ∨ { ∼ (p ∨ Q) } is a
990(a) Tautology
991(b)Contradiction
992(c) Contingency
993(d) None of these Ans. : (a)
994Q. 63 [(p ∨ ∼ Q) → p ] and (p ∨ Q) are
995(a) Equivalent
996(b) Not equivalent
997(c) Sometime equivalent sometime not equivalent
998(d) Cannot say Ans. : (a)
999Q. 64 Find the negation of
1000“There exists a dog that is of 25 years old”
1001(a) Some dogs are not 25 years old
1002(b) All dogs are 25 years old
1003(c) Every dog is 25 year old
1004(d) Every dog is not 25 years old Ans. : (d)
1005Q. 65 Universal quantification is true if
1006(a) All of its substitution instances are true
1007(b) Some of its substitution instances are true
1008(c) None of its substitution instances are true (d)
1009None of these Ans. : (a)
1010Q. 66 Negate the statement
1011“All patients are admitted to ICU”
1012(a) At least one patient is admitted to ICU.
1013(b) At least one patient is not admitted to ICU.
1014(c) All patients are not admitted to ICU.
1015(d) No patient is admitted to ICU . Ans. : (c)
1016Q. 67 Negate the statements.
1017“Some birds sing well”
1018(a) At least one bird does not sing well
1019(b) All birds sing well
1020(c) None of the birds does not sing well
1021(d) No birds sing well Ans. : (d)
1022Q. 68 Which of the option represents symbolically the following statement ? “All birds
1023are beautiful”. B(x) : x is a bird M(x) : x is beautiful
1024(a) ( ∀ x) [B (x) ∨ M (x)]
1025(b) ( ∀ x [B (x) → M (x)]
1026(c) ∼ [( ∃ x), {B (x) ∧ M (x)}]
1027(d) None of these Ans. : (b)
1028Q. 69 Some politician are cheater
1029p (x) : x is a politician C (x) : x is a cheater
1030(a) ( ∃ x) [p (x) ∨ C (x)]
1031(b) ( ∃ x) [p (x) ↔ C (x)]
1032(c) ( ∃ x) [p (x) ∧ C (x)]
1033(d) ( ∃ x) [p (x) ∧ ∼ C (x)] Ans. : (c)
1034Q. 70 If n (A) = 24, n (B) = 69 and n (A ∪ B) = 81
1035Then what is n (A ∩ B) ?
1036(a) 36
1037(b) 12
1038(c) 6
1039(d) 14 Ans. : (b)
1040Q. 71 If n (A) = 7, n (B) = 15 and n (A ∩ B) = 5 then what is n (A ∪ B) ?
1041(a) 18
1042(b) 22
1043(c) 17
1044(d) 16 Ans. : (c)
1045Q. 72 Tell whether the statement is true or false ?
1046{4, 6, 13} = {0, 4, 6, 13}
1047(a) True (b)False Ans. : (b)
1048Q. 73 Let A = {a, b, {c, d}, e}. How many elements does A contain ?
1049(a) 5
1050(b) 4
1051(c)5
1052(d) None of these Ans. : (b)
1053Q. 74 Let A = {2, {4, 5}, 4}. Which statement is correct
1054(a) {5} is an element of A
1055(b) {5} is an element of A
1056(c) {4, 5} is an element of A
1057(d) {5} is subset of A Ans. : (c)
1058Q. 75 Which of these are finite ?
1059(a) {x | x is even}
1060(b) {x | x < 5}
1061(c) {1, 2, 3 ..........}
1062(d){1, 2, 3, .......... 999, 1000} Ans. : (d)
1063Q. 76 Which of these set is not a null set ?
1064(a) A = {x | 6x = 24 and 3x = 1}
1065(b) B = {x | x + 10 = 10}
1066(c) C = {x | x is a man older than 200 years }
1067(d) D = {x | x < x} Ans. : (b)
1068Q. 77 Let S = {1, 2, 3}. How many subset does S contains
1069(a) 6
1070(b) 3
1071(c)8
1072(d)5 Ans. : (c)
1073Q. 78 Let D ⊂ E, suppose a ∈ D and b ∉ E. Which of the following statement must
1074be true
1075(a) C ∈ D
1076(b)b ∈ D
1077(c) a ∈ E
1078(d) a ∉ D Ans. : (c)
1079Q. 79 Determine whether the given events are disjoint. “Being a teenager and being
1080a prime minister of India”
1081(a) Yes
1082(b)No Ans. : (a)
1083Q. 80 If A and B are two sets and A ∩ B = φ then A and B are called
1084(a) Universal set
1085(b) Disjoint set
1086(c) Complement of a set
1087(d) None of these Ans. : (b)
1088Q. 81 Every set is a subset of itself
1089(a) True (b)False Ans. : (a)
1090Q. 82 The Empty set is a subset of any set
1091(a) False (b)True Ans. : (b)
1092Q. 83 Let A = {a, b, {a, b}, {(a, b}}}
1093Identify each of the following statement as a true or false with justification
1094(i) a ∈ A, True as a is an element of A
1095(ii) {a} ∈ A, False as {a} is not an element but a subset of A
1096(iii){a, b} ∈ A, True as {a, b} is an element of A
1097(iv){{a, b }} ⊆ A, True it is subset of A
1098(v) {a, b} ⊆ A, True it is subset of A
1099(vi){a, {b}} ⊆ A, False as {b} is not an element of A
1100Q. 84 Determine whether each of the following statement is true or false for arbitrary
1101sets A, B, C. Justify your answer.
1102(i) If A ∈ B and B ⊆ C, then A ∈ C :True, as being an element of B, it should also belongs to C
1103as B is a subset of C.
1104(ii) If A ∈ B and B ⊆ C then A ⊆ C False, as A is not a subset but an element of B
1105(iii)If A ⊆ B and B ∈ C, then A ∈ C. False e.g. A = {a}, B = {a, b}, C = {{a, b}}
1106(iv)If A ⊆ B and B ∈ C, then A ⊆ C.
1107Q. 85 If A = {2, 4, 6, 8, 10} and B = {1, 2, 6, 8, 12, 15} What is A ∪ B
1108(a) {1, 2, 4, 6, 8, 10, 12, 15}
1109(b) {1, 2, 4, 6, 8, 10}
1110(c) {6, 8, 10, 15}
1111(d) φ Ans. : (a)
1112Q. 86 If A = {2, 4, 6, 8, 10} and B = {1, 2, 6, 8, 12, 15} Then find A ∩ B
1113(a) {2, 4, 6, 8}
1114(b) {2, 6, 8}
1115(c) { φ }
1116(d) {1, 2, 4, 6, 8} Ans. : (b)
1117Q. 87 If A = {2, 4, 6, 8, 10} and B = {1, 2, 6, 8, 12, 15}
1118Then find A ⊕ B
1119(a) {2, 4, 6, 8}
1120(b){2, 6, 8}
1121(c) {1, 4, 10, 15}
1122(d) φ Ans. : (c)
1123Q. 88 If A = {2, 4, 6, 8, 10} and B = {1, 2, 6, 8, 12, 15}
1124Then find A – B
1125(a) {2, 4, 6, 8}
1126(b){4, 10}
1127(c) {1, 4, 12, 15}
1128(d) φ Ans. : (b)
1129Q. 89 A ⊕ A = ?
1130(a) A
1131(b) A 1
1132(c) A –1
1133(d) φ Ans. : (d)
1134Q. 90 A ⊕ B = ?
1135(a) A ∪ B
1136(b) A – B
1137(c) A ∪ B – A ∩ B
1138(d) A ∩ B Ans. : (c)
1139Q. 91 If U = {1, 2, 3,............100} and A = {2, 4, 6, 8, 10...}
1140Then A ′ = ?
1141(a) U
1142(b)A ∪ U
1143(c) A ∩ U
1144(d){1, 3, 5, 7, 9, 11.....100} Ans. : (d)
1145Q. 92 If A = {a, b, {a, c}, φ }, then determine
1146A – {a, c}
1147(a) {b}
1148(b) {b, {a, c}, φ }
1149(c){a, c}
1150(d) φ Ans. : (b)
1151Q. 93 If A = {a, b, {a, c}, φ }, then determine {{a,c}} – A = ?
1152(a) {a, b}
1153(b) φ
1154(c){a, c}
1155(d) {a, b, {a, c}} Ans. : (b)
1156Q. 94 If A = {a, b, {a, c}, φ }, then determine A– {{a, b}} = ?
1157(a) A
1158(b) φ
1159(c) {a, b, {a, c}}
1160(d) {a, b} Ans. : (a)
1161Q. 95 If A = {a, b, {a, c}, φ }, then determine
1162{a, c} – A = ?
1163(a) {b}
1164(b) {a}
1165(c) {c}
1166(d) φ Ans. : (c)
1167Q. 96 If A = [1, 1, 1, 2, 2, 3] and B = [1, 2, 2, 2, 3, 3] are two multiset then find
1168A ∪ B = ?
1169(a) [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3 ]
1170(b) [1, 1, 1, 2, 2, 2, 3, 3]
1171(c) [1, 1, 2, 2, 3, 3]
1172(d) [1, 1, 1, 2, 2, 3, 3] Ans. : (b)
1173Q. 97 If A = [1, 1, 1, 2, 2, 3] and B = [1, 2, 2, 2, 3, 3] are two multiset then find
1174A ∩ B = ?
1175(a) [1, 2, 2, 3]
1176(b) [1, 2, 3]
1177(c) [1, 1, 2, 2, 3, 3]
1178(d) [ φ ] Ans. : (a)
1179Q. 98 If A = [1, 1, 1, 2, 2, 3] and B = [1, 2, 2, 2, 3, 3] are two multiset then find
1180A – B = ?
1181(a) [1, 2, 3]
1182(b)[1, 2, 2, 3, 3]
1183(c) [1, 1]
1184(d) [1, 1, 2, 3, 3] Ans. : (c)
1185Q. 99 If A = [1, 1, 1, 2, 2, 3] and B = [1, 2, 2, 2, 3, 3] are two multiset then find
1186A + B = ?
1187(a) [1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3]
1188(b) [1, 1, 1, 1, 2, 2, 2, 3, 3, 3]
1189(c) [1, 2, 3]
1190(d) [ φ ] Ans. : (a)
1191Q. 100 If p → q then converse is
1192(a) p ′ → q ′
1193(b) q → p
1194(c) p → q
1195(d)None of these Ans. : (b)
1196Q. 101 If p → q the contrapositive is,
1197(a) q → p
1198(b)~ q → ∼ p
1199(c) q ↔ p
1200(d)None of these Ans. : (b)
1201Q. 102 What is the converse of the following statements
1202“If it rains, then I carry an umbrella”
1203(a) If I carry an umbrella then it rains
1204(b) If it do not rains then I will not carry an umbrella
1205(c) If I do not carry umbrella then it does not rains
1206(d) If I do not carry an umbrella then it rains Ans. : (a)
1207Q. 103 What is the contrapositive of the statement in Q. 102
1208(a) If I carry an umbrella then it rains
1209(b) If it do not rain then I will not carry an umbrella
1210(c) If I do not carry an umbrella then it does not rain
1211(d) If I do not carry an umbrella then it rains Ans. : (c)
1212Q. 104 A statement form which always assumes the truth value T irrespective of the
1213truth value assigned to its variables are called
1214(a) Contradiction
1215(b) Tautology
1216(c) Contingency
1217(d) None of these Ans. : (b)
1218Q. 105 A statement form which always assumes the truth value F irrespective of the
1219truth value assigned to it variables are called
1220(a) Contradiction
1221(b) Tautology
1222(c) Contingency
1223(d) None of these Ans. : (a)
1224Q. 106 The modus ponens or the rule of detachment is,
1225(a) Valid inference
1226(b) Inconsistent inference
1227(c) Satisfiable but not valid
1228(d) Invalid inference Ans. : (a)
1229Q. 107 If S (x) : x is a student
1230I (x) : x is intelligent
1231‘ H (x) : x is honest
1232Represent the statement “Every intelligent student is not honest”
1233(a) ( ∃ x) [S (x) ∧ I (x) ∧ ∼ H (x)]
1234(b) ( ∀ x) [S (x) ∨ I (x) → ∼ H (x)]
1235(c) ( ∀ x) [S (x) ∧ I (x) ← H (x)]
1236(d) ( ∃ x) [S (x) ∧ I (x) ∨ H (x)] Ans. : (a)
1237Q. 108 If A = [a, a, b, c, d, d, d, e] B = [a, b, d, f, g]
1238C = [b, c, e, e, g, h, h] D = [a, d, d, e, f, f, g, h]What is the
1239value of A ∪ B
1240(a) [a, a, b, c, d, f, g]
1241(b) [a, a, b, c, d, d, d, e, f, g]
1242(c) [a, a, a, b, d, f, g]
1243(d) [a, b, d, f, g, a] Ans. : (b)
1244Q. 109 If A = [a, a, b, c, d, d, d, e] B = [a, b, d, f, g]
1245C = [b, c, e, e, g, h, h] D = [a, d, d, e, f, f, g, h] What is the value of C ∩ D
1246(a) [b, c, e, e,]
1247(b)[a, d, e, g]
1248(c) [e, g, h]
1249(d)None of these. Ans. : (c)
1250Q. 110 If A = [a, a, b, c, d, d, d, e] B = [a, b, d, f, g]
1251C = [b, c, e, e, g, h, h] D = [a, d, d, e, f, f, g, h] What is the value of A – D
1252(a) [a, a, b, c]
1253(b)[a, b, c, d]
1254(c) [e, g, h]
1255(d)None of these Ans. : (c)
1256
1257
1258Sr. No. Question Option 1 Option 2 Option 3 Option 4 Ans
12591 The union of two sets A & B is the set containing of all elements which are in A, or in B, or in both sets A & B. TRUE FALSE 1
12602 The intersection of two sets A & B is the set consisting of elements which are in A as well as in B. TRUE FALSE 1
12613 The intersection of two sets A & B is the set containing of all elements which are in A, or in B, or in both sets A & B. TRUE FALSE 2
12624 The union of two sets A & B is the set consisting of elements which are in A as well as in B. TRUE FALSE 2
12635 If A={1,2,3,4,5,6,7,8,9,10} , B= {1,3,5,7,9} Then A – B= {1,2,3,4,5,6,7,8,9,10} {2,,4,6,8,10} {2,3,4,5,6,7,8,9} {2,4,6,8} 2
12646 A’=U-A TRUE FALSE 1
12657 A – B = A ∩ B’ TRUE FALSE 1
12668 A symmetric difference with B = (A – B ) U (B – A ) TRUE FALSE 2
12679 A symmetric difference with B = (A – B ) ∩ (B – A ) TRUE FALSE 2
126810 A – B = A’ ∩ B’ TRUE FALSE 2
126911 if A={Φ}, B= {a,Φ,{Φ}} then A symmetric difference with B= {a,Φ} {Φ} {a,{Φ}} {a,Φ,{Φ}} 3
127012 De Morgan’s law state that (AUB)’=A’∩ B’ (AUB)=(BUA) (A∩B)’=A’U B’ Both a & c 4
127113 AU(B’∩C) = (AUB’)∩(AUC) TRUE FALSE 1
127214 Let A and B be two sets. If each element of set A is an element of set B then A is called subset of B. TRUE FALSE 1
127315 A’U(B’∩C’) = (AUB’)∩(AUC) TRUE FALSE 2
127416 . Let A and B be two sets. If each element of set A is not an element of set B then A is called subset of B. TRUE FALSE 2
127517 The set having no element is called Empty set Null set Void set All of the above 4
127618 If a finite set S has n elements, then power of set S has ___________ elements 4n 3n 2n 1n 3
127719 The set having no element is called class of set void set Power set All of the above 2
127820 AU(BUC)=_____________ (AUB)∩C (A∩B)∩C (AUB)UC A’UB’UC’ 3
127921 (A∩B)UA =__________ AUB AUA A Both b & c 4
128022 If A & B are non empty sets then ________ A∩B subset of A subset of AUB and A∩Bsubset of Bsubset of AUB AUB subset of A subset of A∩B and AU B subset of B subset of A∩B Both 1 and 2 None of the above 1
128123 If A and B are two sets then |AUB|= |A|+|B|-|A∩B| |AUB|= |A|+|B|+|A∩B| |AUB|= |A|+|B| |AUB|= |A|-|B| 1
128224 If S is a set containing n elements then number of elements in power set of S,i.e P(S)_____ n 2n 2n n2 3
128325 If A and B are disjoint sets then__________ AUB = Φ AUB = A AUB = B A∩B = Φ 2
128426 If A and B are two sets then which statements is true? (A – B ) and (B – A ) are equal sets (A – B ) and (B – A ) are disjoint sets (A – B ) = A (B – A ) = B 3
128527 If A and B are two sets then which of the following statement is true? a) (A – B ) , (A∩B) and (B – A ) are pairwise disjoint sets. (A – B ) U (B – A ) = A ∩ B (A – B ) ∩ (B – A ) = A ∩ B A – B ) U (B – A ) = A U B 1
128628 If A and B are two sets then which of the following statement is true? (A – B ) ∩ (A∩B) ∩ (B – A ) = AUB (A – B ) U (A∩B) U (B – A ) = AUB (A – B ) ∩ (A∩B) ∩ (B – A ) = A∩B (A – B ) ∩ (AUB) ∩ (B – A ) = A∩B 2
128729 If A and B are two sets then symmetric difference of A and B is__________ (A – B ) ∩ (B – A ) (A – B ) U (B – A ) (A – B ) - (B – A ) (B – A ) – (A – B ) 2
128830 If A and B are two sets then symmetric difference of A and B is__________ (A U B ) ∩ (B ∩ A ) (A U B ) U (B ∩ A ) (A U B ) - (B ∩ A ) (B ∩ A ) – (A U B ) 3
128931 If A and B are two sets and A ≠ B such that A ∩ B = A then _________ A is subset of B B is subset of A both 1 and 2 None of the above 1
129032 If A and B are two sets and A ≠ B such that A U B = A then _________ A is subset of B B is subset of A both 1 and 3 None of the above 2
129133 For sets A and B , (A∩B)∩A = ___________ A B A∩B None of the above 3
129234 For sets A and B , (AUB)UA = ___________ A B AUB None of the above 3
129335 For any three non empty sets A, B, C |AUBUC|= ____________ |A|+ |B|+|C|+ |A∩B|+|A∩C|+|B∩C|+|A∩B∩C| |A|+ |B|+|C|- |A∩B|-|A∩C|-|B∩C|-|A∩B∩C| |A|+ |B|+|C|- |A∩B|-|A∩C|-|B∩C|+|A∩B∩C| |A|+ |B|+|C| 3
129436 If (A∩B)’= B’ then_________ A is subset of B B is subset of A AUB = B None of the above 2
129537 If A={1,2,3,4}, B={4,5,6,7} then A – B=__________ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 3
129638 If A={1,2,3,4}, B={4,5,6,7} then B – A=__________ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 2
129739 If A={1,2,3,4}, B={4,5,6,7} then A ∩ B=__________ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 4
129840 If A={1,2,3,4}, B={4,5,6,7} then A U B=__________ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 1
129941 If X is universal set, Φ is empty set and A is any set then A∩B = A X Φ None of the above 1
130042 If A={a,b,{a,c},Φ} then A- {a,c}= ___________ {a,b,Φ} {b,{a,c},Φ} {a,b,{a,c},Φ} None of the above 2
130135 For any three non empty sets A, B, C |AUBUC|= ____________ |A|+ |B|+|C|+ |A∩B|+|A∩C|+|B∩C|+|A∩B∩C| |A|+ |B|+|C|- |A∩B|-|A∩C|-|B∩C|-|A∩B∩C| |A|+ |B|+|C|- |A∩B|-|A∩C|-|B∩C|+|A∩B∩C| |A|+ |B|+|C| 3
130244 If s={1,2} and P(S)={Φ,{1},{2},{1,2}}then which statement is true? 1 is subset of S 1 belongs to S {1} belongs to S None of the above 2
130345 If s={1,2} and P(S)={Φ,{1},{2},{1,2}}then which statement is true? {1} belongs to P(S) Φ belongs to P(S) Φ is subset of to P(S) all 1,2,3 4
130446 X is universal set ,Φ is empty set and A is any non empty set if A'∩X= Φ then______ A=X A=Φ A'=X None of the above 1
130547 X is universal set ,Φ is empty set and A is any non empty set if (A∩B)'=B' then______ A is subset of B B is subset of A A U B = B None of the above 2
130648 For any two sets A and B which statement is true ? B=(A- B)U (A∩B) B=(B-A)U (A∩B) B=(A-B)U(B-A) B=(B-A)∩(A∩B) 1
130749 If A={{a,b}} then which statement is true? A belongs to A a belongs to A {a,b}belongs to A 3
130850 If A={1,2,3,4,5}, B={2,3,4} then which statement is true B belongs to A A belongs to B A is subset of B B is subset of B 4
130951 For any non empty set A , Which statement is true A has no subset A has atleast one subset A has atleast 2 subsets None of the above 3
131052 If A= {1,2,3,4}, B={4,5,6,7 } then A-B is ______ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 3
131153 If A= {1,2,3,4}, B={4,5,6,7 } then B-A is ______ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 2
131254 If A= {1,2,3,4}, B={4,5,6,7 } then A∩B is ______ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 4
131355 If A= {1,2,3,4}, B={4,5,6,7 } then AUB is ______ {1,2,3,4,5,6,7} {5,6,7} {1,2,3} {4} 1
131456 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |A| is 125 50 83 35 3
131557 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |B| is 125 50 83 35 2
131658 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |C| is 125 50 83 35 4
131759 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |A∩B| is 50 83 16 35 3
131860 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |A∩C| is 16 11 7 35 2
131961 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |B∩C| is 16 11 7 35 3
132062 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |A∩B∩C| is 16 11 7 1 4
132163 Consider a set S of integers from 1 to 250. A denotes the set of integers divisible by 3,B denotes the set of integersdivisible by 5 and C denotes the set of integers divisible by 7 then |AUBUC| is 83 50 35 135 4
132264 Number of elelments divisible by 3or 5 but not by 7 135 100 35 117 2
132365 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |A| is 2000 1000 666 400 2
132466 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |B| is 2000 1000 666 400 3
132567 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |C| is 1000 666 400 285 3
132668 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |D| is 1000 666 400 285 4
132769 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |A∩B| is 400 285 333 142 3
132870 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |A∩C| is 200 333 142 133 1
132971 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |A∩D| is 142 133 95 57 1
133072 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |B∩D| is 142 57 95 133 3
133173 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |B∩C| is 142 57 95 133 4
133274 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |C∩D| is 142 57 95 133 2
133375 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |A∩B∩C| is 57 66 47 28 2
133476 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |A∩B∩D| is 66 47 28 19 2
133577 If S denotes the set of integers between 1 to 2000 and A is the set of integers divisible by 2, B is the set of integers divisible by 3, C is the set of integers divisible by 5, D is the set of integers divisible by 7 ,then |A∩C∩D| is 66 47 28 19 3
133678 There are many clouds in the sky but it did not rain, p:There are many clouds in the sky , q:It rain then pVq p˄q pV(~q) p˄(~q) 4
133779 I will get first class if and only if I study well and score above 80 in mathematics ,p:I will get first class,q: I study well,r: Score above 80 in maths q↔p (p˄q)↔r (p˄r)↔q p↔(q˄r) 4
133880 computers are cheap but softwares are costly, p:computers are cheap,q:softwares are costly then pVq p˄q pV(~q) p˄(~q) 2
133981 If 'p' stands for 'I run fast' and'q' stands for 'I shall win', then symbolic form of ,'I do not run fast' p (~q) q (~q) 2
134082 If 'p' stands for 'I run fast' and'q' stands for 'I shall win', then symbolic form of ,'If I run fast, I shall win' p→q q→p p↔q (~p)→(~q) 1
134183 If 'p' stands for 'I run fast' and'q' stands for 'I shall win', then symbolic form of ,'I run fast or I shall not win' pVq p˄q pV(~q) (~p)Vq 3
134284 If 'p' stands for 'I run fast' and'q' stands for 'I shall win', then symbolic form of ,'I run fast and I shall win' pVq p˄q p→q q→p 2
134385 If 'p' stands for 'I run fast' and'q' stands for 'I shall win', then symbolic form of ,'I neither run fast nor I shall win' (~p)˄(~q) (~p)V(~q) p˄(~q) (~p)˄q 1
134486 ^ denotes set membership union AND a relation between sets 3
134587 v denotes set membership OR AND a relation between sets 2
134688 ∩ denotes set membership intersection conjunction negation 2
134789 Ø denotes set membership empty set conjunction negation 2
134890 € denotes set membership union AND OR 1
1349
1350((MARKS)) (1/2/3...) 1
1351((QUESTION)) If p˄q is T then
1352((OPTION_A)) P is T , q is T
1353((OPTION_B)) P is F, q is T
1354((OPTION_C)) P is T, q is F
1355((OPTION_D)) P is F , q is F
1356((CORRECT_CHOICE)) (A/B/C/D) B
1357
1358
1359((MARKS)) (1/2/3...) 1
1360((QUESTION)) If p˅q is F then
1361((OPTION_A)) P is T , q is F
1362((OPTION_B)) P is F , q is T
1363((OPTION_C)) P is F , q is F
1364((OPTION_D)) P is T, q is F
1365((CORRECT_CHOICE)) (A/B/C/D) C
1366((EXPLANATION)) (OPTIONAL)
1367
1368
1369
1370((MARKS)) (1/2/3...) 1
1371((QUESTION)) If p˅ is F then
1372
1373((OPTION_A)) P is T, q is F
1374((OPTION_B)) P is F, q is T
1375((OPTION_C)) P is F, q is F
1376((OPTION_D)) P is T, q is F
1377((CORRECT_CHOICE)) (A/B/C/D) b
1378((EXPLANATION)) (OPTIONAL)
1379
1380((MARKS)) (1/2/3...) 1
1381((QUESTION)) The statement is Logically equivalent to
1382
1383((OPTION_A))
1384
1385((OPTION_B))
1386
1387((OPTION_C))
1388
1389((OPTION_D))
1390
1391((CORRECT_CHOICE)) (A/B/C/D) D
1392
1393((MARKS)) (1/2/3...) 1
1394((QUESTION)) is logically equivalent to
1395
1396((OPTION_A))
1397
1398
1399((OPTION_B))
1400
1401((OPTION_C))
1402
1403((OPTION_D))
1404
1405((CORRECT_CHOICE)) (A/B/C/D) C
1406
1407
1408
1409
1410((MARKS)) (1/2/3...) 1
1411((QUESTION)) is logically equivalent to
1412
1413((OPTION_A)) P
1414((OPTION_B)) Tautology
1415((OPTION_C)) Contradiction
1416((OPTION_D)) None of these
1417((CORRECT_CHOICE)) (A/B/C/D) A
1418
1419((MARKS)) (1/2/3...) 1
1420((QUESTION)) Let p: Mohan is rich
1421 q: Mohan is Happy
1422Then the statement : Mohan is rich but happy in symbolic form
1423((OPTION_A))
1424
1425((OPTION_B))
1426
1427((OPTION_C))
1428
1429((OPTION_D))
1430
1431((CORRECT_CHOICE)) (A/B/C/D) D
1432((EXPLANATION)) (OPTIONAL)
1433
1434((MARKS)) (1/2/3...) 1
1435((QUESTION)) For the universe of all integers if E(x) denotes the predicate x is even symbolic representation of the statement: at least one integer is even is
1436((OPTION_A))
1437
1438((OPTION_B))
1439
1440((OPTION_C))
1441
1442((OPTION_D))
1443
1444((CORRECT_CHOICE)) (A/B/C/D) b
1445((EXPLANATION)) (OPTIONAL)
1446
1447((MARKS)) (1/2/3...) 1
1448((QUESTION)) The negation of the following statement: is
1449
1450((OPTION_A))
1451
1452((OPTION_B))
1453
1454((OPTION_C))
1455
1456((OPTION_D)) None of these
1457((CORRECT_CHOICE)) (A/B/C/D) C
1458((EXPLANATION)) (OPTIONAL)
1459
1460((MARKS)) (1/2/3...) 1
1461((QUESTION)) is logically equivalent to
1462
1463((OPTION_A)) p
1464((OPTION_B)) Tautology
1465((OPTION_C)) Contradiction
1466((OPTION_D)) None of these
1467((CORRECT_CHOICE)) (A/B/C/D) B
1468((EXPLANATION)) (OPTIONAL)
1469
1470((MARKS)) (1/2/3...) 1
1471((QUESTION)) The converse of is
1472
1473((OPTION_A))
1474
1475((OPTION_B))
1476
1477((OPTION_C))
1478
1479((OPTION_D))
1480
1481((CORRECT_CHOICE)) (A/B/C/D)
1482A
1483((EXPLANATION)) (OPTIONAL)
1484
1485((MARKS)) (1/2/3...) 1
1486((QUESTION)) Let p: I will get job
1487 q:I pass the exam
1488then the statement form: I will get a job only if I
1489 pass the exam in symbolic is
1490((OPTION_A))
1491
1492((OPTION_B))
1493
1494((OPTION_C))
1495
1496((OPTION_D))
1497
1498((CORRECT_CHOICE)) (A/B/C/D)
1499A
1500((EXPLANATION)) (OPTIONAL)
1501
1502((MARKS)) (1/2/3...) 1
1503((QUESTION)) Let p: It rains
1504 q:I go for a walk
1505then the statement form: If it rains I will not
1506in symbolic is
1507((OPTION_A))
1508
1509((OPTION_B))
1510
1511((OPTION_C))
1512
1513((OPTION_D))
1514
1515((CORRECT_CHOICE)) (A/B/C/D) C
1516((EXPLANATION)) (OPTIONAL)
1517
1518((MARKS)) (1/2/3...) 1
1519((QUESTION)) If A={ a, b, {a,c}, }then A-{a,c}
1520
1521((OPTION_A)) { a, b, }
1522
1523((OPTION_B)) { b, {a,c}, }
1524
1525((OPTION_C)) { c, {b,c}}
1526((OPTION_D)) { a, c, {a,c}, }
1527
1528((CORRECT_CHOICE)) (A/B/C/D) A
1529((EXPLANATION)) (OPTIONAL)
1530
1531((MARKS)) (1/2/3...) 1
1532((QUESTION)) Determine which of the following statement is true
1533((OPTION_A)) If and then
1534
1535((OPTION_B)) If and then
1536
1537((OPTION_C)) If and then
1538
1539((OPTION_D)) If and then
1540
1541((CORRECT_CHOICE)) (A/B/C/D) A
1542((EXPLANATION)) (OPTIONAL)
1543
1544((MARKS)) (1/2/3...) 1
1545((QUESTION)) If A={ , a} then is
1546
1547((OPTION_A))
1548
1549((OPTION_B)) A
1550((OPTION_C)) P(A)
1551((OPTION_D)) { }
1552
1553((CORRECT_CHOICE)) (A/B/C/D) D
1554((EXPLANATION)) (OPTIONAL)
1555
1556((MARKS)) (1/2/3...) 1
1557((QUESTION)) If A is a set containing 5 distinct element, then the cardinality of the power set A is
1558((OPTION_A)) 64
1559((OPTION_B)) 16
1560((OPTION_C)) 32
1561((OPTION_D)) 128
1562((CORRECT_CHOICE)) (A/B/C/D) C
1563((EXPLANATION)) (OPTIONAL)
1564
1565((MARKS)) (1/2/3...) 1
1566((QUESTION)) If A={1,2,4,6,8} , B={2,4,5,9} then is the set
1567
1568((OPTION_A)) {1, 4, 5, 6, 8}
1569((OPTION_B)) {1, 5, 6, 8, 9}
1570((OPTION_C)) {1, 2, 5, 8, 9}
1571((OPTION_D)) {1, 6, 8, 9}
1572((CORRECT_CHOICE)) (A/B/C/D) B
1573((EXPLANATION)) (OPTIONAL)
1574
1575((MARKS)) (1/2/3...) 2
1576((QUESTION)) If is T and r is F, then truth values of p and q are
1577((OPTION_A)) P is T, q is T
1578((OPTION_B)) P is T, q is F
1579((OPTION_C)) P is F, q is F
1580((OPTION_D)) P is F, q is T
1581((CORRECT_CHOICE)) (A/B/C/D) A
1582((EXPLANATION)) (OPTIONAL)
1583
1584
1585
1586((MARKS)) (1/2/3...) 2
1587((QUESTION)) If is F then
1588
1589((OPTION_A)) P is T, q is T
1590((OPTION_B)) P is T, q is F
1591((OPTION_C)) P is F, q is F
1592((OPTION_D)) P is F, q is T
1593((CORRECT_CHOICE)) (A/B/C/D) D
1594((EXPLANATION)) (OPTIONAL)
1595
1596((MARKS)) (1/2/3...) 2
1597((QUESTION)) Disjunctive normal form of is
1598
1599((OPTION_A))
1600
1601((OPTION_B))
1602
1603((OPTION_C))
1604
1605((OPTION_D))
1606
1607((CORRECT_CHOICE)) (A/B/C/D) A
1608((EXPLANATION)) (OPTIONAL)
1609
1610((MARKS)) (1/2/3...) 2
1611((QUESTION)) is logically equivalent to
1612
1613((OPTION_A))
1614
1615((OPTION_B))
1616
1617((OPTION_C)) Tautology
1618((OPTION_D))
1619
1620((CORRECT_CHOICE)) (A/B/C/D) C
1621((EXPLANATION)) (OPTIONAL)
1622
1623((MARKS)) (1/2/3...) 2
1624((QUESTION)) If p(x)=prime number and o(x) is=x is odd, then the symbolic representation of the statement “All prime number are not odd”
1625((OPTION_A))
1626
1627((OPTION_B))
1628
1629((OPTION_C))
1630
1631((OPTION_D))
1632
1633((CORRECT_CHOICE)) (A/B/C/D) D
1634((EXPLANATION)) (OPTIONAL)
1635
1636((MARKS)) (1/2/3...) 2
1637((QUESTION)) Among the integers 1 to 300, the number of integers which are divisible of 3 and 5 is
1638
1639((OPTION_A)) 100
1640((OPTION_B)) 120
1641((OPTION_C)) 130
1642((OPTION_D)) 140
1643((CORRECT_CHOICE)) (A/B/C/D) D
1644((EXPLANATION)) (OPTIONAL)
1645
1646((MARKS)) (1/2/3...) 2
1647((QUESTION)) Among the integers 1 to 300, the number of integers which are divisible of 3 but not 5 is
1648((OPTION_A)) 100
1649((OPTION_B)) 60
1650((OPTION_C)) 80
1651((OPTION_D)) 140
1652((CORRECT_CHOICE)) (A/B/C/D) C
1653((EXPLANATION)) (OPTIONAL)
1654
1655((MARKS)) (1/2/3...) 2
1656((QUESTION)) It was found that in first year class of computer science, consists of 80 students, 50 know cobol, 55 know C, 37 know C and Cobol, 28 know C and Pascal, 25 know pascal and cobol, 7 knows one of these languages, Then the number of students who know all the three language is
1657((OPTION_A)) 10
1658((OPTION_B)) 12
1659((OPTION_C)) 15
1660((OPTION_D)) 20
1661((CORRECT_CHOICE)) (A/B/C/D) B
1662((EXPLANATION)) (OPTIONAL)
1663
1664((MARKS)) (1/2/3...) 2
1665((QUESTION)) In a survey conducted for 2000 persons, It was found that 1750 drank tea, 820 drank coffee, 625 drank both, then the number of persons who drank neither is
1666((OPTION_A)) 65
1667((OPTION_B)) 55
1668((OPTION_C)) 45
1669((OPTION_D)) 60
1670((CORRECT_CHOICE)) (A/B/C/D) B
1671((EXPLANATION)) (OPTIONAL)
1672
1673((MARKS)) (1/2/3...) 2
1674((QUESTION)) Using principal of mathematical induction, n2+2n is
1675((OPTION_A)) Divisible of 3
1676
1677((OPTION_B)) Divisible of 6
1678
1679((OPTION_C)) Divisible of 4
1680
1681((OPTION_D)) Divisible of 2
1682
1683((CORRECT_CHOICE)) (A/B/C/D) A
1684((EXPLANATION)) (OPTIONAL)
1685
1686((MARKS)) (1/2/3...) 2
1687((QUESTION)) Using induction principal if
1688
1689Then
1690((OPTION_A))
1691
1692((OPTION_B))
1693
1694((OPTION_C))
1695
1696((OPTION_D))
1697
1698((CORRECT_CHOICE)) (A/B/C/D) C
1699((EXPLANATION)) (OPTIONAL)
1700
1701((MARKS)) (1/2/3...) 2
1702((QUESTION)) Let A={1,2,{1,2}} then p(p(A)) has
1703((OPTION_A)) 22 element
1704((OPTION_B)) 23 element
1705((OPTION_C)) 24 element
1706((OPTION_D)) 28 element
1707((CORRECT_CHOICE)) (A/B/C/D) D
1708((EXPLANATION)) (OPTIONAL)
1709
1710((MARKS)) (1/2/3...) 2
1711((QUESTION)) IF U={1,2,3,……9,10}, A={1,2,3,4,5}B={1,2,4,8}, C={1,2,3,5,7}then the set is
1712
1713((OPTION_A)) {1,2,3,5,8}
1714((OPTION_B)) {1,2,3,4,5,8}
1715((OPTION_C)) {1,2,4,5,7,8}
1716((OPTION_D)) {3,4,7,8}
1717((CORRECT_CHOICE)) (A/B/C/D) B
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740UNIT:2 Relation & Functions
1741
1742Q. 1 The binary relation S = f (empty set) on set A = {1, 2, 3} is ,
1743(a) Neither reflexive nor symmetric (b) Symmetric and reflexive
1744(c) Transitive and reflexive (d) Transitive and symmetric
1745Ans. : (d)
1746Q. 2 The number of binary relation on a set with n elements is ________.
1747(a) n2 (b) 2n (c) 2n2 (d) None of these Ans. : (c)
1748Q. 3 If A is a finite set with n elements, then number of elements in the largest
1749equivalence relation of A is,
1750(a) 1 (b) n (c) n + 1 (d) n2 Ans. : (d)
1751Q. 4 The number of functions from on m element set to an n element set is,
1752(a) m + n (b)mn (c) nm (d) m * m Ans. : (c)
1753Q. 5 The number of equivalence relations of the set {1, 2, 3, 4} is,
1754(a) 4 (b) 15 (c) 16 (d) 24 Ans. : (b)
1755Q. 6 If R be a non-empty relation on a collection of sets defined by ARB if and only
1756if A Ç B = f Then
1757(a) R is reflexive and transitive
1758(b) R is symmetric and not transitive
1759(c) R is equivalence relation
1760(d) R is not reflexive and not symmetric Ans. : (b)
1761Q. 7 If R be a symmetric and transitive relation on a set A then
1762(a) R is reflexive and hence an equivalence relation
1763(b) R is reflexive and hence a partial order
1764(c) R is not reflexive and hence not an equivalence relation
1765(d) None of these Ans. : (d)
1766Q. 8 A relation R defined on a set A = {1, 2, 3, 4} by R= {(1, 1), (2, 2) (3, 3) } is
1767(a) Reflexive (b)Symmetric
1768(c) Transitive (d)None of these Ans. : (d)
17691
1770UNIT:2 Relation & Functions
1771Q. 9 If a relation R is defined by,
1772R = { (a, b) | a divides b; a , b Î N }
1773Then R is,
1774Reflexive (b)Symmetric (c) Transitive (d) None of these
1775Q. 10 A relation R is defined on a set N by,
1776R = {(a, b) : | a – b | is divisible by 5} is,
1777(a) Reflexive (b)Symmetric (c) Transitive (d) All of these
1778Ans. : (d)
1779Q. 11 A Relation R is defined on the set N as,
1780{ (a, b) : a, b are both odd } is
1781(a)Reflexive (b) Symmetric (c) Transitive (d) None of these
1782Ans. : (b)
1783Q. 12 If R is an equivalence relation on a set A, then R–1 is,
1784(a) Reflexive (b)symmetric (c) Transitive (d) All of these
1785Ans. : (d)
1786Q. 13 “n / m” means that n is a factor of m, then the relation ‘T’ is,
1787(a) Reflexive and symmetric
1788(b) Transitive and symmetric
1789(c) Reflexive, transitive, symmetric
1790(d) Reflexive, transitive, not symmetric Ans. : (d)
1791Q. 14 The number of distinct relation on set of 3 elements is,
1792(a) 8(b) 9 (c)18 (d)512 Ans. : (d)
1793Q. 15 A = {string of 0’s and 1’s } Relation d on A is defined as xdy if x is a substring
1794of y (e.g. 01d 101), Then d is,
1795(a) Symmetric (b)Anti symmetric
1796(c) Equivalence (d)Reflexive and symmetric Ans. : (b)
1797Q. 16 If relation R over {a, b, c} is given by,
1798R = {(a, a), (a, b), (b, a), (b, b), (c, c)}
17992
1800UNIT:2 Relation & Functions
1801Then R is,
1802(a) Reflexive (b)Symmetric (c) Transitive (d) All of these
1803Ans. : (d)
1804Q. 17 The domain and range are same for
1805(a) Constant function (b) Identify function
1806(c) Absolute value function (d) Greatest integer function Ans. : (b)
1807Q. 18 Which of the following is a partition of the set
1808S = {1, 2, 3, 4, 5, 6}
1809(a) [{1, 3, 5}, {2, 4}, {3, 6}] (b) [{1, 5}, {2}, {3, 6}]
1810(c) [{1, 5}, {2}, {4}, {1, 5}, {3, 6}] (d) [{1, 2, 3, 4, 5, 6}] Ans. : (d)
1811Q. 19 If R = {(1, 1), (3, 1), (2, 3), (4, 2)} then which of the following represents R2,
1812where R2 is R composite R.
1813(a) {(1, 1), (3, 1), (2, 3), (4, 2)} (b) {(1, 1), (9, 1), (4, 9), (16, 4)}
1814(c) {(1, 3), (3, 3), (3, 4), (3, 2)} (d) {(1, 1), (2, 1), (4, 3) (3, 1)} Ans. : (d)
1815Q. 20 The number of distinct reflexive and symmetric relations that can be defined as
1816a 3 element set is,
1817(a) 3(b) 4 (c)6 (d)8 Ans. : (d)
1818Q. 21 If P (A) be the collection of all subsets of A = {a, b, c} and R be a relation
1819defined as “x is disjoint from y” over p (A) then the number of elements in R
1820is,
1821(a) 8 (b) 9 (c) 17 (d) 11 Ans. : (d)
1822Q. 22 Let R1 and R2 be two equivalence relation on a set consider the following
1823assertion.
1824I. R1 È R2 is an equivalence relation.
1825II. R1 Ç R2 is an equivalence relation.
1826Which of the following is, correct ?
1827(a) Both assertions are true (b) I is true but II is not true
1828(c) II is true but I is not true (d) Neither I nor II is true Ans. : (c)
18293
1830UNIT:2 Relation & Functions
1831Q. 23 The binary relation
1832R = {(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}
1833on the set A = {1, 2, 3, 4} is,
1834(a) Reflexive, symmetric and transitive
1835(b) Neither reflexive nor irreflexive but transitive
1836(c) Irreflexive, symmetric and transitive
1837(d) Irreflexive and antisymmetric Ans. : (b)
1838Q. 24 A relation on the integers 0 through 4 ? is defined by R = {(x, y) : x + y £ 2x}
1839Which of the properties listed below applies to this relation
1840Transitive II. Symmetric III. Reflexive
1841(a) I only (b) III only (c) I and III (d) II and III Ans. : (c)
1842Q. 25 If R and S are a non empty relation in a set A. which of the following is false.
1843(a) If R and S are transitive, then R È S is transitive
1844(b) If R and S are transitive, then R Ç S is transitive
1845(c) If R and S are symmetric, then R È S is symmetric
1846(d) If R and S are reflexive, then R È S is reflexive Ans. : (a)
1847Q. 26 Let R be an equivalence relation on the set
1848{1, 2, 3, 4, 5, 6} given by,
1849{(1, 1), (1, 5), (2, 2), (2, 3), (2, 6), (3, 2), (3, 3), (3, 6), (4, 4), (5, 1) (5,5), (6, 2),
1850(6, 3), (6,6 )}
1851The partition induced by R is,
1852(a) {1, 2, 3, 4, 5, 6} (b) {{1, 3, 5, 6}, {2, 4}}
1853(c) {{1, 5}, {2, 3, 6}, {4}} (d) {{1, 2, 3, 4}, {5, 6} } Ans. : (c)
1854Q. 27 If A = {1, 2, 3} then relation
1855S = {(1, 1), (2, 2)} is
1856(a) Symmetric only (b) Anti symmetric only
1857(c) Both symmetric and anti symmetric (d) Equivalence relation
1858Ans. : (c)
1859Q. 28 If A = {1, 2, 3, 4}. Let ~ = {(1, 2), (1, 3), (4, 2)}
18604
1861UNIT:2 Relation & Functions
1862Then ~ is,
1863(a) Not anti symmetric (b) Transitive
1864(c) Reflexive (d) Symmetric Ans. : (b)
1865Q. 29 If R = {(1, 2), (2, 3), (3, 3)} be a relation defined on
1866A = {1, 2, 3} then R. R = R2 is,
1867(a) R itself (b) {(1, 2), (1, 3), (3, 3)}
1868(c) {(1, 3), (2, 3), (3, 3)} (d) {(2, 1), (1, 3), (2, 3)} Ans. : (c)
1869Q. 30 The universal relation A ´ A is,
1870(a) An equivalence relation
1871(b) Antisymmetric
1872(c) Partial ordering relation
1873(d) Not symmetric and not Antisymmetric Ans. : (a)
1874Q. 31 Total number of different partition of a set having 4 elements are ?
1875(a) 16 (b) 8 (c) 15 (d) 4 Ans. : (c)
1876Q. 32 A partition of {1, 2, 3, 4, 5} is the family
1877(a) {(1, 2), (3, 4), (3, 5)}(b) {f, (1, 2), (3, 4), 5}
1878(c) {(1, 2, 3), {5}} (d) {{1, 2}, {3, 4, 5}} Ans. : (d)
1879Q. 33 The less than relation, < on real is
1880(a) A partial ordering since it is asymmetric and reflexive.
1881(b) A partial ordering since it is antisymmetric and reflexive.
1882(c) Not a partial ordering because it is not antisymmetric and not reflexive .
1883(d) None Ans. : (c)
1884Q. 34 A relation R is defined on the set of integers as xRy if f (x + y) is even. Which
1885of the statement is true,
1886(a) R is not an equivalence relation.
1887(b) R is an equivalence relation having one equivalence class
1888(c) R is an equivalence relation having two equivalence classes.
1889(d) R is an equivalence relation having three equivalence classes.
1890Ans. : (c)
18915
1892UNIT:2 Relation & Functions
1893Q. 35 The time complexity of computing the transitive closure of a binary relation on
1894a set of n element is known to be
1895(a) O (n) (b) O (n log n) (c) O (n3/2) (d) O(n3) Ans. : (d)
1896Q. 36 The subset relation on a set of set is,
1897(a) Partial ordering
1898(b) An equivalence relation
1899(c) Transitive and symmetric relation
1900(d) Transitive and Anti symmetric Ans. : (a)
1901Q. 37 If R = {(a, b), (a, c), (a, d), (a, a), (b, c) } then what is R–1
1902(a) {(b, a), (a, c), (d, a), (a, a), (b, c)}
1903(b) {(b, a), (c, a), (d, a), (c, b)}
1904(c) {(b, a), (c, a), (d, a),(a, a), (c, b)}
1905(d) {(a, b), (a, c), (a, d), (a, a), (b, c)} Ans. : (c)
1906.
1907Q. 38 If R and S are two non empty set theÈ = ?
1908(a) È (b) Ç (c)Å (d) None of these Ans. : (b)
1909Q. 39 If R and S are the two non empty set then Ç= ?
1910(a) È (b) Ç (c)Å (d) None of these Ans. : (a)
1911Q. 40 If R and S are two non empty relation the (RC)C = ?
1912(a) R (b) Rc (c) R2 (d) None of these Ans. : (a)
19136
1914UNIT:2 Relation & Functions
1915Q. 41 If R an S are two non empty relation then (R È S )C = ?
1916(a) Rc È Sc (b) Rc Ç Sc (c) Rc + Sc (d) None of these
1917Ans. : (b)
1918Q. 42 If R and S are two non empty relation. Then (R Ç S)c = ?
1919(a) Rc È Sc (b) Rc Ç Sc (c) Rc + Sc (d) None Ans. : (a)
1920Q. 43 Let A = {1, 2, 3, 4} and B = {a, b, c}
1921Let R = {(1, a), (3, a), (3, c)} then domain of R is
1922(a) {1, 2, 3, 4} (b) {1, 3} (c) {1, 2, 3} (d) {1, 4} Ans. : (b)
1923Q. 44 With the same data of Q. 43, what is range of R?
1924(a) {a, b, c} (b){a, b} (c) {a, c } (d) None of these Ans. : (c)
1925Q. 45 Let A = {2, 3, 4, 6}. Let R be relation on A such that R = {(a, b) | a = b + 1 or b
1926= 2a} then what is R = ?
1927(a) {(3, 2), (4, 3), (2, 2), (2, 4), (3, 6)}
1928(b) {(3, 2), (4, 3), (2, 4)}
1929(c) {(3, 2), (4, 3), (2, 4), (3, 6)}
1930(d) None Ans. : (c)
1931Q. 46 Let A = {2, 3, 4, 6}. Let R be a relation on A such that S = {(a, b) | a divides b }
1932(a) {(2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}
1933(b) {(2, 4), (2, 6), (3, 6)}
1934(c) {(2, 2), (2, 4), (2, 6), (3, 6)}
1935(d) None of these Ans. : (a)
1936Q. 47 A = {a, b, c, d}
1937R1 = {(a, a), (a, b), (b, d)}
1938R2 = {(a, d), (b, c), (b, d), (c, d)}
1939Find R1 R2 = ?
1940(a) {(a, d), (a, c)} (b) {(a, d), (a, c), (a, a)}
1941(c) {(a, d), (a, c), (a, b)} (d) None of there Ans. : (a)
1942Q. 48 Based on the data of Q. 47, what is R2 R1
19437
1944UNIT:2 Relation & Functions
1945(a) {(b, c)} (b) {(a, b)} (c) {(c, d)} (d) {(c, b)} Ans. : (c)
1946Q. 49 Based on the data of Q. 47, what is = ?
1947(a) {(a, a), (a, b), (a, c)} (b) {(a, a), (a, b), (a, d)}
1948(c) {(a, a), (a, b), (a, c), (b, d)} (d) None of these Ans. : (b)
1949Q. 50 Based on the data of Q. 47, what is
1950(a) {(b, b), (c, c) (c, d), (a, a)} (b) {(b, b), (c, c), (c, d)}
1951(c) {(c, c), (a, a), (b, b)} (d) None of these Ans. : (b)
1952Q. 51 Let A = {a, b, c, d} and let
1953MR =
1954Then R = ?
1955(a) {(a, a), (a, b), (b, c), (b, d), (c, c), (c, d), (d, a), (d, c)}
1956(b) {(a, a), (a, b), (b, c), (b, d)}
1957(c) {(c, c), (c, d), (d, a), (d, c)}
1958(d) None of these Ans. : (a)
1959Q. 52 So what is R = ?
1960Fig. Q. 52
1961(a) {(2, 3), (3, 2), (3, 4), (3, 5), (4, 3), (4, 4), (4, 5)}
1962(b) {(2, 2), (3, 3), (3, 2), (3, 4)}
1963(c) {(2, 3), (3, 4), (3, 5), (4, 3), (4, 5)}
1964(d) None of these Ans. : (a)
1965Q. 53 In a relation if every element of the set is related to itself then the relation is
1966called
1967(a) Reflexive (b) Symmetric (c) Transitive (d) None
1968Ans. : (a)
1969Q. 54 In a relation R if (a, b) Î R and (b, a) Î R, then the relation is called
19708
1971UNIT:2 Relation & Functions
1972(a) Reflexive (b) Symmetric (c) Transitive (d) None
1973Ans. : (b)
1974Q. 55 In a relation R if (a, b) Î R and (b, a) Ï R then the relation is called
1975(a) Reflexive (b)Symmetric
1976(c) Asymmetric (d)Antisymmetric Ans. : (c)
1977Q. 56 In a relation R if (a, b) Î R and (b, a) Î R, then a = b. The relation R called
1978(a) Reflexive (b)Symmetric
1979(c) Asymmetric (d)Antisymmetric Ans. : (d)
1980Q. 57 In a relation R if (a, b) Î R and (b, c) Î R then (a, c) Î R R is called
1981(a) Reflexive (b)Symmetric
1982(c) Transitive (d)Antisymmetric Ans. : (c)
1983Q. 58 In a relation R is reflexive, symmetric and transitive then relation R is called
1984(a) Equivalence (b) Universal
1985(c) Poset (d)None of these Ans. : (a)
1986Q. 59 Let A = {1, 2, 3, 4} and let
1987R = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (2, 3), (3, 2), (3, 3), (4, 4)}
1988How many equivalence class R have
1989(a) 3 (b) 2 (c) 1 (d) 4 Ans. : (b)
1990Q. 60 Let A = {a, b, c, d}, p = {{a, b}, {c}, {d}}
1991Then find R = ?
1992{(a, a), (a, b), (b, a), (b, b), (c, c), (d, d)}
1993{(a, a), (b, b), (c, d)}
1994{(a, a), (b, c), (a, d), (b, d)}
1995None of these Ans. : (a)
1996Q. 61 If A = {1, 2, 3, 4, 5, 6} and R = {(x, y) | |x – y| = 2}
1997Find R = ?
1998(a) {(3, 1), (4, 2), (5, 3), (6, 4)}
1999(b) {(1, 3), (2, 4), (3, 5), (4, 6)}
20009
2001UNIT:2 Relation & Functions
2002(c) {(1, 3), (3, 1), (2, 4), (4, 2), (3, 5), (5, 3), (4, 6), (6, 4)}
2003(d) None of these Ans. : (c)
2004Q. 62 A binary relation R on set A is partial order set (Poset) if
2005(a) R is reflexive, symmetric and transitive
2006(b) R is reflexive, transitive and Antisymmetric
2007(c) R is reflexive, symmetric and Antisymmetric
2008(d) None is these Ans. : (b)
2009Q. 63 Partial ordered set can be represented graphically by
2010(a) Diagraph (b)Hasse diagram
2011(c) Lattice (d)Graph Ans. : (b)
2012Q. 64 Let (A, £) be a poset and if every pair of elements in the subset are related
2013then it is called
2014(a) Lattice (b) Chain (c) Antichain (d) None of these
2015Ans. : (b)
2016Q. 65 Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and consider the Hasse diagram given
2017below.
2018Fig. Q. 65
2019Find G LB {2, 3} = ?
2020(a) 1(b) 2 (c)3 (d)4 Ans. : (a)
2021Q. 66 Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and consider the Hasse diagram given
2022below.
202310
2024UNIT:2 Relation & Functions
2025Fig. Q. 66
2026GLB {2, 7} = ?
2027(a) 3(b) 2 (c)1 (d)6 Ans. : (c)
2028Q. 67 Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and consider the Hasse diagram given
2029below.
2030Fig. Q. 67
2031GLB {5, 8} = ?
2032(a) 3(b) 6 (c)2 (d)1 Ans. : (a)
2033Q. 68 Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and consider the Hasse diagram given
2034below.
2035Fig. Q. 68
203611
2037UNIT:2 Relation & Functions
2038LUB {3, 2} = ?
2039(a) 6(b) 9 (c)5 (d)3 Ans. : (c)
2040Q. 69 Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and consider the Hasse diagram given
2041below.
2042Fig. Q. 69
2043LUB {4, 8} = ?
2044(a) 5(b) 10 (c) 9 (d) 6 Ans. : (b)
2045Q. 70 Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and consider the Hasse diagram given
2046below.
2047Fig. Q. 70
2048LUB {3, 5} = ?
2049(a) 3(b) 4 (c)5 (d)2 Ans. : (c)
2050Q. 71 Hasse diagrams are drawn for
2051(a) Partially ordered set (b) Lattices
205212
2053UNIT:2 Relation & Functions
2054(c) Boolean Algebra (d) None of these Ans. : (a)
2055Q. 72 A self complemented distributive lattice is called
2056(a) Boolean Algebra (c) Complete Lattice
2057(c) Modular Lattice (d) Self dual Lattice Ans. : (a)
2058Q. 73 Which of the following is not a Lattice
2059(a) (b) (c) (d)
2060Fig. Q. 73
2061Ans. : (b)
2062Q. 74 Let D30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation I be partial ordering on D30.
2063The all lower bounds of 10 and 15 respectively are,
2064(a) 1, 3 (b) 1, 5 (c) 1, 3, 5 (d) None of these Ans. : (b)
2065Q. 75 Let D30 {1, 2, 3, 5, 6, 10, 15, 30} and relation I be a partial ordering on D30.
2066The all upper bounds of 10 and 15 respectively is
2067(a) 30 (b) 15 (c) 10 (d) 6 Ans. : (a)
2068Q. 76 Let D30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation I be a partial ordering on D30.
2069The lub of 10 and 15 respectively is,
2070(a) 30 (b) 15 (c) 10 (d) 6 Ans. : (a)
2071Q. 77 The maximal and minimal elements of this poset are
207213
2073UNIT:2 Relation & Functions
2074Fig. Q. 77
2075(a) maximal 5, 6 : Minimal 2
2076(b) maximal 5, 6 : Minimal 1
2077(c) maximal 3, 5 : Minimal 1, 6
2078(d) None of these Ans. : (c)
2079Q. 78 The greatest and least elements of the poset are
2080Fig. Q. 78
2081(a) greatest 4, 5; least 1,2
2082(b) greatest 5; least 1
2083(c) greatest none ; least none
2084(d) None of these Ans. : (c)
2085Q. 79 Different partially ordered sets may be represented by the same Hasse
2086diagram, if they are
2087(a) Same (b)Lattices with same order
2088(c) Isomorphic (d) Order isomorphic Ans. : (d)
2089Q. 80 Let L be a set with a relation R which is transitive, antisymmetric and reflexive
2090and for any two elements a, b Î L. Let least upper bound Lub (a, b) and the
2091greatest lower bund GLB (a, b) exist. Which of the following is / are true.
2092(a) L is a poset (b) L is a Boolean algebra
2093(c) L is a lattices (d) None of these Ans. : (a and c)
2094Q. 81 In the lattice defined by the Hasse diagram given below, how many
2095complements does the element ‘e’ have
209614
2097UNIT:2 Relation & Functions
2098Fig. Q. 81
2099(a) 2(b) 3 (c)0 (d)1 Ans. : (b)
2100Q. 82 Let X = {2, 3, 6, 12, 24} and £ be the partial order defined by X < Y if x divides
2101Y. Number of edges in the Hasse diagram of (X, £) is
2102(a) 3(b) 4 (c)5 (d)None Ans. : (b)
2103Q. 83 The absorption law is defined as
2104(a) a* (a * b) = b (b) a * (a Å b) = b
2105(c) a * (a * b) = a Å b (d) a * (a Å b) = a Ans. : (d)
2106Q. 84 If lattice (C, £ ) is a complemented chain, then
2107(a) | C | £ | (b)|C| £ 2 (c) |C| > 1 (d) None of these
2108Ans. : (b)
2109Q. 85 If set A = {1, 2, 3, 4}, then ordered pairs in the relation determined by the
2110Hasse diagram in the figure given below are described as.
2111Fig. Q. 85
2112{(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}
2113{(1, 1), (2, 2), (3,3), (4, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}
2114both (a) and (b)
2115None of these Ans. : (a)
2116Q. 86 Matrix of the partial order whose hasse diagram is given below.
2117(a)
211815
2119UNIT:2 Relation & Functions
2120Fig. Q. 86
2121(b) (c)
2122(d) None of these Ans. : (c)
2123Q. 87 Principle of duality is defined as
2124(a) £ is replaced by ³ (b) LUB becomes GLB
2125(c) All properties are unaltered when £ is replaced by ³.
2126(d) All properties are unaltered when £ is replaced by ³ other than 0 and 1. Q. 88 Every finite subset of Lattice has
2127(a) A LUB and a GLB (b) Many LUB s and a GLB
2128(c) Many LUB and many GLB s (d) None of these Ans. : (a)
2129Q. 89 Which statement is not true for the Hasse diagram.
2130(a) All arrow heads are omitted
2131(b) All loops are omitted as it indicate reflexive
2132(c) An arc is not present in the diagram if it is due to transitivity
2133(d) There is an edge present which indicate symmtricity Ans. : (d)
2134Q. 90 From the given Hasse diagram find the relation ?
2135Fig. Q. 90
2136(a) {(2, 2), (2, 4), (2, 6), (3, 6),(3, 3), (6, 6), (4,4)}
2137(b) {(2, 4), (4, 2), (2, 6), (6, 2), (3, 6), (6, 3)}
2138(c) {(2, 2), (2, 4), (3, 6), (3, 3), (4, 4)}
2139(d) None of these Ans. : (a)
214016
2141UNIT:2 Relation & Functions
2142Q. 91 From the given Hasse diagram. Find the relation R.
2143Fig. Q. 91
2144(a) {(1, 2)} (b) {(1, 1), (2, 2)}
2145(c) {(1, 1), (2, 2), (1, 2)} (d) None of these Ans. : (c)
2146Q. 92 If set A contains n elements and set B contains m elements then number of
2147elements in A ´ B is
2148(a) m + n (b)n – m (c) m * n (d) n/m Ans. : (c)
2149Q. 93 If A, B and C are non empty set then A ´ (B Ç C) is = ?
2150(a) (A ´ B) È (A ´ C) (b) (A ´ B) Ç (A ´ C)
2151(c) (A ´ B) Ç C (d) (A ´ C) Ç B Ans. : (b)
2152Q. 94 If A, B and C are non empty set then A ´ (B È C) is = ?
2153(a) (A ´ B) È (A ´ C) (b) (A ´ B) Ç (A ´ C)
2154(c) (A ´ B) È C (d) (A ´ C) È B Ans. : (a)
2155Q. 95 If R is a relation defined from set A to set B then
2156(a) R = A ´ B (b)R Ì A ´ B
2157(c) R Ì B ´ A (d)A ´ B Ì R Ans. : (b)
2158Q. 96 If A = {1, 2, 3, 4}, B = {1, 4, 6, 8, 9} and aRb if b = a2 then the relation matrix
2159can be represented as.
2160(a) (b)
2161(c) (d) Ans. : (a)
2162Q. 97 If A = {1, 2, 3, 4, 6} aRb iff a/b (a divide b) then relation R is,.
2163(a) {(1, 3), (1, 4), (2, 6), (2, 4)}
2164(b) {(2, 4), (2, 6), (1, 1), (4, 4), (6, 6)}
2165(c) {(1, 1), (2, 2), (2, 6), (2, 4), (3, 3), (4, 4), (5, 5) }
216617
2167UNIT:2 Relation & Functions
2168(d) {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4),
2169(6, 6)} Ans. : (d)
2170Q. 98 If A = {1, 2, 3, 4}
2171If R = {(a, b) | (a – b) } is multiple of 2 then R = ?
2172(a) {(1, 3), (2, 4)} (b) {(1, 3), (3, 1), (2, 4), (4, 2)}
2173(c) {(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (3, 1), (2, 4), (4, 2)}
2174(d) None of these Ans. : (c)
2175Q. 99 If A = {1, 2, 3, 4, 5, 6} and R on A is defined by
2176R = {(a, b); a – b = 2x, where x Î N, N is the set of natural numbers then
2177{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
2178{(3, 1), (4, 2), (5, 3), (5, 1), (6, 4), (6, 2)}
2179{(1, 1), (3, 1), (2, 2), (4, 2), (5, 3), (5, 1), (6, 4)}
2180None of these Ans. : (b)
2181Q. 100 If A = {1, 2, 3} and Relation R is denoted by the given diagraph then R is +
2182Fig. Q. 100
2183(a) Reflexive (b) Symmetric
2184(c) Equivalence relation (d) Poset Ans. : (c)
2185Q. 101 If f is a function from set A to set B then which is true ?
2186(a) A is known as domain set (b) A is known as co-domain set
2187(c) A is range (d) None of these Ans. : (a)
2188Q. 102 If f : A ® B is a function then which is true
2189(a) Range of f is subset of A (b) Range of f is subset of B
2190(c) Both a and b (d) None of these Ans. : (b)
2191Q. 103 If f : A ® B is a function then which is true.
2192(a) f (a1) = b and f (a1) = c Þ b = c
2193(b) f(a1) = b and f (a2) = b Þ a1 = a2
219418
2195UNIT:2 Relation & Functions
2196(c) $ a Î A | f (a) Ï B.
2197(d) None of these Ans. : (a)
2198Q. 104 If f : A ® B is a function and range of f = B, then f is,
2199(a) one to one (b)on to
2200(c) Many to one (d) Many to many Ans. : (b)
2201Q. 105 If f : A ® B and g : B ® c are two functions then composite of f and g is
2202(a) gof : A ® C (b)fog : A ® C
2203(c) gof : C ® A (d)fog : C ®A Ans. : (a)
2204Q 106 The function f : N ® N defined by f (n) = 2n + 3 is
2205(a) Suggestive (b)Bijective
2206(c) Injective (d)None of these Ans. : (c)
2207Q. 107 The domain and range are same for
2208(a) Constant function (b) Identity function
2209(c) Absolute value function (d) Greatest Integer function Ans. : (b)
2210Q. 108 The function f : Z ® Z2 given by f (x) = x2 is,
2211(a) one – one (b) on to
2212(c) one to one and onto (d) None of these Ans. : (b)
2213Q. 109 Let A = {1, 2, 3, 4} and B = {0, 1, – 1, 2} and several sets of ordered pairs be
2214specified as
2215I. {(1, 0), (2, 1), (3, – 1), (4, 2)} II. {(1, 0), (2, –1), (3, 2)}
2216III. {(4, 1), (3, 2), (2, 3), (1, 4)} IV. {(2, 1), (3, 0), (1, –1), (3, 1), (4, 2)}
2217V. {(2, 0), (1, – 1), (3, 2), (4, 1)}
2218Which of the sets of ordered pairs are graphs of a function from A ® B = ?
2219(a) II and III (b)III and IV
2220(c) I and V (d)IV and V Ans. : (c)
2221Q. 110 Which of the sets of ordered pairs are onto functions from A ® B
2222(a) II and III (b)III and IV
2223(c) I and V (d)IV and V Ans. : (c)
222419
2225UNIT:2 Relation & Functions
2226Q. 111 The function f : R – {2} ® R defined by,
2227f x) = (x2 + 2x) / (x – 2) is,
2228(a) One to one and onto (b) one to one but not onto
2229(c) Neither one to one nor onto (d) Not one to one but onto.
2230Ans. : (c)
2231Q. 112 If set A has n elements then number of functions that can be defined from A
2232into A is,
2233(a) n2 (b) n! (c) nn (d) n Ans. : (c)
2234Q. 113 If f(A) = B i.e. range of f is equal to the co-domain of f then f is,
2235(a) Sarjective (on to) (b) Injective (one to one)
2236(c) Bijective (one to one onto) (d) None of these Ans. : (a)
2237Q. 114 Identify which is not a function ?
2238(a) 10 0a (b) 10 0a
223920 0b 20 0b
224030 0c 30 0c
2241(c) 0 0 (d) 10 0a
22420 0 20
22430 0 30 0b
224440 0c
2245Ans. : (c)
2246Q. 115 The function f : R ® R defined as f (x) = 1/x. Identify the type of function it is,
2247(a) Equivalent (b)Composite
2248(c) Partial (d)Identify Ans. : (c)
2249Q. 116 The function f : R ® R defined as f (x) = , Identify which type of function it is,
2250(a) Equivalent (b)Composite
2251(c) Partial (d)Identify Ans. : (c)
225220
2253UNIT:2 Relation & Functions
2254Q. 117 If f : A ® B and g : C ® D be functions’ :’ and if A = C,B = D then identify the
2255function,
2256(a) Equivalent (b)Composite
2257(c) Partial (d)Identify Ans. : (a)
2258Q. 118 Identify which function it is :
2259a0 a
2260b0 b
2261c0 g
2262d0 d
2263e0
2264(a) onto (b)one to one
2265(c) one to one onto (d) None of these Ans. : (a)
2266Q. 119 The set A has 3 elements and set B has 4 elements then number of injections
2267that can be defined from A into B is
2268(a) 144 (b) 12 (c) 24 (d) 64 Ans. : (c)
2269Q. 120 If n ³ 2, then number of surjection that can be defined from {1, 2, 3,……n} onto
2270{1, 2} is,
2271(a) 2n (b) nP2 (c) 2n (d) 2n– 2 Ans. : (d)
2272Q. 121 Number of bijective function from set A to itself when A contain 106 elements
2273is,
2274(a) 106 (b) 1062 (c) 106! (d) 2106 Ans. : (b)
2275Q. 122 If f : Z ® Z be defined as f (x) = x2, x Î Z, then function f is
2276(a) bijection (b)injection
2277(c) surjection (d)None of these Ans. : (d)
2278Z = {1, 2, 3, 4, 5, 6}
2279f (x), f(1) = 1 Î Z
2280f (2) = 4 Î Z
2281f (3) = 9 Ï Z. Some of the element is not have image. So it is not a function
2282Q. 123 If : R ® R is a function defined by f (x) = 10x – 7. If g = f–1, then g (x) = ?
228321
2284UNIT:2 Relation & Functions
2285(a) (b)
2286(c) (d) Ans. : (c)
2287Q. 124 If | A | = m and | B | = n, the number of possible relation R : A ® B is,
2288(a) mn (b)(mn)2 (c) 2m + n (d) 2mn Ans. : (d)
2289Q. 125 If function f : R ® R is given by f(x) = x2 + 2x – 3 and function g : R ® R is
2290given by g (x) = 3x – 4 then gof (x) is given by,
2291(a) 9x2 + 18x + 5 (b) 3x2 + 6x – 13
2292(c) x2 + x – 7 (d)x2 – 5 x – 1 Ans. : (b)
2293Q. 126 To have inverse for the function f, f is,
2294(a) one to one (b) onto
2295(c) one to one onto (d) identify Ans. : (b)
2296Q. 127 Let f : R ® R be defined by,
2297f(x) = £££³
2298Then the value of f (– 1. 75) + f (0.5) + f (1. 5)
2299(a) 0(b) 2 (c)1 (d)–1 Ans. : (c)
2300Q. 128 Let Z denote the set of all integers define f : Z ® Z by,
2301f (x) =
2302then f is
2303(a) onto but not one to one (b) one to one but not onto
2304(c) one to one but not onto (d) Neither onto one nor onto Ans. : (a)
2305Q. 129 If f : A ® B is a bijective function then f–1 of f = ?
2306(a) f O f–1 (b)f
2307(c) f–1 (d)IA (Identity) Ans. : (d)
2308Q. 131 Identify which of the following relations are functions ?
2309I. N = {(x, y) | y = x2, x Î {–1, 0, 1, 2, 3}}
2310II. p = {(x, y) | y2 = x, x Î {4, 9, 16}}
2311III. Q = {(x, y) | y = 4x2 – 14, x Î {–1, 1, 2, 3}}
2312(a) I only (b)I and II only
2313(c) I and III only (d) III only Ans. : (c)
231422
2315UNIT:2 Relation & Functions
2316Q. 132 Let f (x) = x + 2, g(x) = x – 2 and h (x) = 3x for x Î R where R = set of real
2317number then find g of (x) = ?
2318(a) x(b) 2x (c) 2x + 1 (d) x2 Ans. : (a)
2319Q. 133 Let f (x) = x + 2, g(x) = x – 2 and h (x) = 3x for x Î R where R = set of real
2320number then find fog (x) = ?
2321(a) x2 (b) x (c)2x (d) 2x + 1 Ans. : (b)
2322Q. 134 Let f (x) = x + 2, g(x) = x – 2 and h (x) = 3x for x Î R where R = set of real
2323number then find fof (x) = ?
2324(a) x + 2 (b)x + 3 (c) x + 4 (d) x Ans. : (c)
2325Q. 135 Let f (x) = x + 2, g(x) = x – 2 and h (x) = 3x for x Î R where R = set of real
2326number then find gog (x) = ?
2327(a) x+4 (b) x – 4 (c) x2 + 4 (d) x2 – 4 Ans. : (b)
2328Q. 136 Let f (x) = x + 2, g(x) = x – 2 and h (x) = 3x for x Î R where R = set of real
2329number then find
2330foh (x) = ?
2331(a) x + 2 (b)3x (c) 3x + 2 (d) x – 2 Ans. : (c)
2332Q. 137 Let f (x) = x + 2, g(x) = x – 2 and h (x) = 3x for x Î R where R = set of real
2333number then find hog (x) = ?
2334(a) 3x + 4 (b)3x – 6 (c) 3x – 4 (d) 3x Ans. : (b)
2335Q. 138 Let f (x) = x + 2, g(x) = x – 2 and h (x) = 3x for x Î R where R = set of real
2336number then find hof (x) = ?
2337(a) 3x + 6 (b)3x – 6 (c) 3x + 2 (d) 3x – 4 Ans. : (a)
2338
2339
2340((MARKS)) (1/2/3...) 1
2341((QUESTION)) 1 The Cartesian Product B x A is equal to the Cartesian
2342product A x B. Is it True or False?
2343((OPTION_A)) True
2344((OPTION_B)) False
2345((OPTION_C)) True if and only if A=B
2346((OPTION_D)) None of the above
2347((CORRECT_CHOICE)) (A/B/C/D) C
2348((EXPLANATION)) (OPTIONAL) Let A = {1, 2} and B = {a, b}. The Cartesian product A x B = {(1, a), (1, b), (2, a), (2, b)} and the Cartesian product B x A = {(a, 1), (a, 2), (b, 1), (b, 2)}. This is not equal to A x B
2349
2350
2351((MARKS)) (1/2/3...) 1
2352((QUESTION)) 2 In a reflexive relation on A
2353((OPTION_A)) each element of A is related to itself
2354((OPTION_B)) if aRband bRcthen aRc
2355((OPTION_C)) The main diagonal of the matrix representing the relation has all 1’s
2356((OPTION_D)) Both B and C
2357((CORRECT_CHOICE)) (A/B/C/D) D
2358((EXPLANATION)) (OPTIONAL)
2359
2360((MARKS)) (1/2/3...) 1
2361((QUESTION)) 3 In a symmetric relation R over A
2362((OPTION_A)) (x A) xRx
2363((OPTION_B)) (x, y A) xRyyRx
2364((OPTION_C)) (x,y,zA) xRyyRzxRz
2365((OPTION_D)) All of these
2366((CORRECT_CHOICE)) (A/B/C/D) B
2367((EXPLANATION)) (OPTIONAL)
2368
2369
2370((MARKS)) (1/2/3...) 1
2371((QUESTION)) 4 Relations that are reflexive, symmetric, and transitive are
2372((OPTION_A)) orderings
2373((OPTION_B)) Partitions
2374((OPTION_C)) equivalence relations;
2375((OPTION_D)) Non-existent
2376((CORRECT_CHOICE)) (A/B/C/D) C
2377((EXPLANATION)) (OPTIONAL)
2378
2379((MARKS)) (1/2/3...) 1
2380((QUESTION)) 5 If R is an antisymmetric relation over A, and if (x, y) R and (y,x)R,
2381Then
2382((OPTION_A)) x A
2383((OPTION_B)) y A
2384((OPTION_C)) x = y
2385((OPTION_D)) x y
2386((CORRECT_CHOICE)) (A/B/C/D) C
2387((EXPLANATION)) (OPTIONAL)
2388
2389((MARKS)) (1/2/3...) 1
2390((QUESTION)) 6 In an equivalence relation R over A
2391((OPTION_A)) (x A) xRx
2392((OPTION_B)) (x, y A) xRyyRx
2393((OPTION_C)) (x,y,zA) xRyyRzxRz
2394((OPTION_D)) All of these
2395((CORRECT_CHOICE)) (A/B/C/D) D
2396((EXPLANATION)) (OPTIONAL)
2397
2398((MARKS)) (1/2/3...) 1
2399((QUESTION)) 7 Which of the following is true
2400((OPTION_A)) If a relation is not reflexive then it is irreflexive
2401((OPTION_B)) If a relation is not symmetric then it is antisymmetric
2402((OPTION_C)) If a relation is antisymmetric then it it asymmetric
2403((OPTION_D)) If a relation is asymmetric then it is antisymmetric
2404((CORRECT_CHOICE)) (A/B/C/D) C
2405((EXPLANATION)) (OPTIONAL)
2406
2407((MARKS)) (1/2/3...) 1
2408((QUESTION)) 8 The partial order relation is
2409((OPTION_A)) Always reflexive and transitive
2410((OPTION_B)) Always symmetric and transitive
2411((OPTION_C)) Always antisymmetric
2412((OPTION_D)) Both A and C
2413((CORRECT_CHOICE)) (A/B/C/D) D
2414((EXPLANATION)) (OPTIONAL)
2415
2416((MARKS)) (1/2/3...) 1
2417((QUESTION)) 9 If R is an antisymmetric relation over A, and if (x, y) R and (y,x)R,
2418Then
2419((OPTION_A)) x A
2420((OPTION_B)) y A
2421((OPTION_C)) x = y
2422((OPTION_D)) x y
2423((CORRECT_CHOICE)) (A/B/C/D) C
2424((EXPLANATION)) (OPTIONAL)
2425
2426((MARKS)) (1/2/3...) 1
2427((QUESTION)) 10 Let R be a relation on set A. If every element of A is related to exactly one element, then the relation is called
2428((OPTION_A)) Reflexive
2429((OPTION_B)) Transitive
2430((OPTION_C)) Partial order
2431((OPTION_D)) Function
2432((CORRECT_CHOICE)) (A/B/C/D) D
2433((EXPLANATION)) (OPTIONAL)
2434
2435((MARKS)) (1/2/3...) 1
2436((QUESTION)) 11 Let R1={<1,2>,<1,3>,<2,3>,<4,3>} and R2={<1,2>,<2,3>,<3,4>} then R2°R2 is
2437((OPTION_A)) {<1,3>,<1,4>,<2,4>,<4,4>}
2438((OPTION_B)) {<1,3>,<1,4>,<2,4>}
2439((OPTION_C)) {<1,3>,<2,4>}
2440((OPTION_D)) None of the above
2441((CORRECT_CHOICE)) (A/B/C/D) C
2442((EXPLANATION)) (OPTIONAL)
2443
2444((MARKS)) (1/2/3...) 1
2445((QUESTION)) 12 Which of the following is true
2446((OPTION_A)) Every relation is function
2447((OPTION_B)) Every function is relation
2448((OPTION_C)) Every equivalence relation not partial order relation
2449((OPTION_D)) Every one-one function has its inverse
2450((CORRECT_CHOICE)) (A/B/C/D) B
2451((EXPLANATION)) (OPTIONAL)
2452
2453((Q 13))If f(x) = -3x - 5, what is the value of f(2) ?
2454 ((A)) 1
2455((B)) -1
2456((C)) 11
2457((D))None of these
2458 Answer is -11
2459((Q))14_//If g(x) = 3x² - 2x - 5, what is the value of g(-1)?
2460 ((A)) -4
2461((B)) -6
2462((C)) 1
2463((D)) 0
2464
2465((Q15))//Which relation is not a function?
2466 ((A)) {(2,5), (3,6), (4,7), (5,8)}
2467((B)) {(6,-2), (-4,6), (-2,4), (1,0)}
2468((C)) {(-1, 5), (-2,5), (-3,5), (-4,5)}
2469((D)) {(0,-2), (1,0), (-1,-3), (0,-1)}
2470
2471((Q16))//Which of the following is true?
2472 ((A)) The relation which is asymmetric is always antisymmetric
2473((B)) Every reflexive relation is symmetric
2474((C)) The relation which is not reflexive is always irreflexive
2475((D)) The relation which is antisymmetric is always asymmetric
2476((Q17))//Let R be the relation in the set of natural no.s N as R={<x,y>|3x+y=11}. Then R-1 is
2477 ((A)) {(0,11) , (1,8) , (2,5) , (3,2)}
2478((B)) {(1, 8) , (2, 5) , (3, 2)}
2479((C)) {(8, 1) , (5, 2) , (2, 3)}
2480((D)) {(11, 0) , (8, 1) , (5, 2) , (2, 3)}
2481Ans : C
2482
2483((Q18))//Number of relations that can be defined in a non-empty set A, having n elements, is
2484 ((A)) n relations
2485((B)) 2n relations
2486((C)) n2 relations
2487((D))2n*n relations
2488 Ans :D
2489
2490((Q19)// The relation on a set A={1,2,3} is R={<1,1>,<1,2>,<2,2>,<2,1>} is
2491 ((A)) reflexive
2492((B)) symmetric
2493((C)) transitive
2494((D)) both B and C
2495 Ans : D
2496
2497((Q20))// Which of the following is true?
2498 ((A)) a relation which is symmetric is not anisymmetric
2499((B)) a relation which is antisymmetric is always asymmetric
2500((C)) a relation which is antisymmetric can be symmetric
2501((D)) none of these
2502 Ans : C
2503
2504((Q21))// The number of distinct relations on a set of 3 elements is:
2505 ((A)) 18
2506((B)) 512
2507((C)) 9
2508((D)) 64
2509Ans :B
2510((Q22))// Transitivity and irreflexive imply:
2511 ((A)) asymmetric
2512((B)) symmetric
2513((C)) equivalence
2514((D)) partial order
2515 Ans :A
2516
2517((Q23)// Find the number of relations from A = {cat, dog, rat} to B = {male , female}
2518 ((A)) 64
2519((B)) 6
2520((C)) 32
2521((D)) 15
2522Ans : A
2523
2524((Q24))// The transitive closure of R = {(1, 1), (1, 4), (2, 1), (2, 2), (3, 3), (4, 4)} is
2525 ((A)) {(1, 1), (1, 4), (2, 1),(2,1), (2, 2), (3, 3), (4, 4)}
2526((B)) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)}
2527((C)) {(1, 1), (1, 4), (2, 1), (2, 2), (3, 3), (4, 4)}
2528((D)) {(1, 1), (1, 4), (2, 1), (2, 2), (3, 2), (4, 4)}
2529 Ans :C
2530
2531((Q25)// If R is a relation on AXA where A is a set of natural numbers such that <a,b>R<c,d> if a+d=b+c then
2532 ((A)) R is partial order
2533((B)) R is equivalence
2534((C)) R is antisymmetric
2535((D)) R is irreflexive
2536Ans : B
2537
2538((Q26))// Which of the following pair is not congruent modulo 7?
2539 ((A)) 25, 56
2540((B)) 10, 24
2541((C)) 11, 31
2542((D)) none
2543Ans : A
2544((Q27))// A partial order relation is
2545 ((A)) reflexive
2546((B)) antisymmetric
2547((C)) transitive
2548((D)) all of these
2549 Ans :D
2550
2551((Q28))//An equivalence relation is
2552 ((A)) reflexive
2553((B)) symmetric
2554((C)) transitive
2555((D)) all of these
2556 Ans : D
2557
2558((Q29))// A relation on set A is
2559 ((A)) element of A
2560((B)) an element of A XA
2561((C)) a subset of A X A
2562((D)) none
2563 Ans : C
2564
2565((Q30))// A relation is not a
2566 ((A)) set of ordered pairs
2567((B)) set of numbers
2568((C)) subset of a Cartesian product
2569((D)) way to express how two sets relate
2570 Ans : B
2571
2572((Q31) The Fibonacci numbers are an instance of a(n)
2573 ((A)) finite set
2574((B)) recursively defined sequence
2575((C)) undecidable set
2576((D)) inductive proof
2577 Ans :B
2578
2579((Q32))// A relation that is reflexive, anti-symmetric and transitive is a
2580 ((A)) function
2581((B)) equivalence relation
2582((C)) partial order
2583((D)) None of these
2584 Ans :C
2585
2586((Q33))The partial order relation in which every pair of elements has GLB and LUB is called
2587 ((A)) equivalence relation
2588((B)) Poset
2589((C)) Lattice
2590((D)) Hasse diagram
2591 Ans :C
2592
2593((Q34))// The partial order relation in which every pair of elements are related is called
2594 ((A)) total order relation
2595((B)) equivalence relation
2596((C)) Lattice
2597((D)) Poset
2598 Ans : A
2599
2600((Q35))// Hasse diagrams represent
2601 ((A)) equivalence relation
2602((B)) partial order relation
2603((C)) lattice always
2604((D)) total order relation always
2605 Ans : B
2606
2607((Q36))// If R is reflexive relation on set A then which is false?
2608 ((A)) In matrix of a relation MR all the diagonal elements will be zero.
2609((B)) In matrix of a relation MR all the diagonal elements will be one.
2610((C)) Diagraph of reflexive relation will have loop for every element of A.
2611((D)) none of these
2612Ans : A
2613
2614((Q37))//) Let R be a symmetric and transitive relation on a set A. Then ?
2615((A)) R is reflexive and hence a partial order
2616((B)) R is reflexive and hence an equivalence relation
2617((C))R is not reflexive and hence not an equivalence relation
2618((D)) None of above
2619Ans : D
2620
2621((Q38))// Use Warshall's algorithm,
2622 ((A)) A)
2623((B)) B)
2624((C)) C)
2625((D)) D)
2626Ans : B
2627
2628((Q39))//The domain D of the relation R is defined as the.... ?
2629((A)) Set of all elements of ordered pair which belongs to R
2630((B)) Set of all last elements of ordered pair which belongs to R
2631((C)) Set of all first elements of ordered pair which belongs to R
2632((D)) None of these
2633Ans : C
2634
2635((Q40))//if f(x) and g(x) are defined on domains A,B respectively then domain of f(x)+g(x) i
2636((A)) AUB
2637((B)) A intersection B
2638((C)) none of these
2639((D)) A-B
2640 Ans : B
2641
2642((Q41))//The number of distinct relation on a set of three element is
2643((A)) 8
2644((B)) 9
2645((C)) 16
2646((D)) 512
2647Ans : D
2648
2649((Q42))//Let S = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}. What is the smallest integer N > 0 such
2650that for any set of N integers, chosen from S, there must be two distinct integers that
2651divide each other?
2652 ((A)) 10
2653((B)) 7
2654((C)) 9
2655((D)) 8
2656Ans : D
2657
2658((Q43))//The relation on set A={1,2,3,…,100} is defined as R={<x,y>|y=x2} is
2659 ((A)) reflexive
2660((B)) irreflexive
2661((C)) asymmetric
2662((D)) none of these
2663Ans : D
2664
2665((Q44))1_//If f xcos x and g( x) x3 , then f o gxis
2666 ((A)) cos x3
2667((B)) 3cos x
2668((C)) cos 3 x
2669((D)) (cos x)3
2670 Ans :A
2671
2672((Q45))1_//The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
2673 ((A)) Reflexive
2674((B)) Transitive
2675((C)) Symmetric
2676((D)) Asymmetric
2677 Ans :B
2678
2679
2680((Q46))1_//A function is a relation from set A to set B whose
2681 ((A)) range is equal to A
2682((B)) Domain is equal to A
2683((C)) |domain|=|A|
2684((D)) both b and c
2685 Ans :D
2686
2687((Q47))1_//The binary relation R = {(0, 0),(1, 1)} on A = {0, 1, 2, 3, } is
2688((A)) Reflexive, Not Symmetric, Transitive
2689((B)) Not Reflexive, Symmetric, Transitive
2690((C)) Reflexive, Symmetric, Not Transitive
2691((D)) Reflexive, Not Symmetric, Not Transitive
2692 Ans :B
2693
2694
2695((Q48))1_//Define a binary relation R = {(0, 1),(1, 2),(2, 3),(3, 2),(2, 0)} on A = {0, 1, 2, 3}. The
2696directed graph (including loops) of the transitive closure of this relation has how many arrows?
2697 ((A)) 16
2698((B)) 12
2699((C)) 8
2700((D)) 6
2701Ans :A
2702
2703
2704((Q49))1_//Let N+ denote the nonzero natural numbers. Define a binary relation R on
2705N+ × N+ by (m, n)R(s, t) if gcd(m, n) = gcd(s, t). The binary relation R is
2706((A)) Reflexive, Not Symmetric, Transitive
2707((B)) Reflexive, Symmetric, Transitive
2708((C)) Reflexive, Symmetric, Not Transitive
2709((D)) Reflexive, Not Symmetric, Not Transitive
2710 Ans :B
2711
2712((Q50))2_//Let N¬¬¬+ denote the natural numbers greater than or equal to 2.
2713Let mRn if gcd(m, n) >1. The binary relation R on N is
2714((A)) Reflexive, Symmetric, Not Transitive
2715((B)) Reflexive, Not Symmetric, Transitive
2716((C)) Reflexive, Symmetric, Transitive
2717((D)) Reflexive, Not Symmetric, Not Transitive
2718Ans : A
2719
2720((Q51))_//Let R and S be binary relations on a set A. Suppose that R is reflexive, symmetric,
2721and transitive and that S is symmetric, and transitive but is not reflexive. Which statement is always true for any such R and S?
2722((A)) R ∪ S is symmetric but not reflexive and not transitive.
2723((B)) R ∪ S is symmetric but not reflexive.
2724((C)) R ∪ S is transitive and symmetric but not reflexive
2725((D)) R ∪ S is reflexive and symmetric.
2726 Ans : D
2727
2728((Q52))2_//Define an equivalence relation R on the positive integers A = {2, 3, 4, . . . , 20} by m R n if the largest prime divisor of m is the same as the largest prime divisor of n. The
2729number of equivalence classes of R is
2730 ((A)) 8
2731((B)) 9
2732((C)) 10
2733((D)) none
2734Ans :A
2735
2736
2737((Q53))2_ssb_end//Let R = {(a, a),(a, b),(b, b),(a, c),(c, c)} be a partial order relation on Σ = {a, b, c}.
2738Let <= be the corresponding lexicographic order on Σ∗. Which of the following is true?
2739((A)) bc <= ba
2740((B)) abbaaacc <= abbaab
2741((C))abbac <= abb
2742((D)) abbac <= abbab
2743 Ans :B
2744
2745((Q54)) 1_ana_start//Let S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. What is the smallest integer K such that any subset of S of size K contains two disjoint subsets of size two, {x1, x2} and {y1, y2}, such that
2746x1+ x2 = y1 + y2 = 9?
2747((A)) 8
2748((B)) 9
2749((C)) 7
2750((D)) 6
2751 Ans :C
2752
2753((Q55))1_//There are K people in a room, each person picks a day of the year to get a free dinner
2754at a fancy restaurant. K is such that there must be at least one group of six people who select the same day. What is the smallest such K if the year is a leap year (366 days)?
2755((A)) 1829
2756((B)) 1831
2757((C)) 1830
2758((D)) 1832
2759 Ans :B
2760
2761((Q56))1_//A mineral collection contains twelve samples of Calomel, seven samples of Magnesite,
2762andN samples of Siderite. Suppose that the smallest K such that choosing K samples
2763from the collection guarantees that you have six samples of the same type of mineral
2764isK = 15. What is N?
2765((A)) 4
2766((B)) 5
2767((C)) 3
2768((D)) 2
2769Ans : A
2770((Q57))1_//What is the smallest N >0 such that any set of N nonnegative integers must have
2771two distinct integers whose sum or difference is divisible by 1000?
2772 ((A)) 502
2773((B)) 520
2774((C)) 5002
2775((D)) 5020
2776 Ans : A
2777
2778((Q58))1_//Let S = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}. What is the smallest integer N >0 such that for any set of N integers, chosen from S, there must be two distinct integers that
2779divide each other?
2780((A)) 10
2781((B)) 7
2782((C)) 9
2783((D)) 8
2784 Ans : D
2785
2786((Q59)) 1_//The binary relation R = {(0, 0), (1, 1)} on A = {0, 1, 2, 3, }is
2787((A)) Reflexive, Not Symmetric, Transitive
2788
2789((B)) Not Reflexive, Symmetric, Transitive
2790
2791((C)) Reflexive, Symmetric, Not Transitive
2792
2793((D)) Reflexive, Not Symmetric, Not Transitive
2794
2795 Ans :B
2796
2797
2798
2799((Q60)) 1_//Define a binary relation R = {(0, 1), (1, 2), (2, 3), (3, 2), (2, 0)} on A = {0, 1, 2, 3}. The directed graph (including loops) of the transitive closure of this relation has
2800
2801((A)) 16 arrows
2802
2803((B)) 12 arrows
2804
2805((C)) 8 arrows
2806
2807((D)) 6 arrows
2808
2809Ans : A
2810
2811
2812
2813((Q61)) 2_//Let N+ denote the nonzero natural numbers. Define a binary relation R on N+ ×N+
2814by (m, n)R(s, t) if gcd(m, n) = gcd(s, t). The binary relation R is
2815
2816((A)) Reflexive, Not Symmetric, Transitive
2817
2818((B)) Reflexive, Symmetric, Transitive
2819
2820((C)) Reflexive, Symmetric, Not Transitive
2821
2822((D)) Reflexive, Not Symmetric, Not Transitive
2823
2824 Ans :B
2825
2826
2827((Q62)) 2_//Let N+2 denote the natural numbers greater than or equal to 2. Let mRnif gcd(m, n) >
28281. The binary relation R on N2 is
2829
2830((A)) Reflexive, Symmetric, Not Transitive
2831
2832((B)) Reflexive, Not Symmetric, Transitive
2833
2834((C)) Reflexive, Symmetric, Transitive
2835
2836((D)) Reflexive, Not Symmetric, Not Transitive
2837
2838Ans : A
2839
2840
2841((Q63)) 2_//Define a binary relation R on a set A to be antireflexiveif xRxdoesn’t hold for any
2842x2 A. The number of symmetric, antireflexive binary relations on a set of ten elements
2843is
2844((A))210
2845
2846((B)) 250
2847
2848((C)) 245
2849
2850((D)) 290
2851
2852Ans :C
2853
2854((Q64)) 2_//Let R and S be binary relations on a set A. Suppose that R is reflexive, symmetric,
2855and transitive and that S is symmetric, and transitive but is not reflexive. Which statement is always true for any such R and S?
2856
2857((A)) R US is symmetric but not reflexive and not transitive.
2858
2859((B)) R US is symmetric but not reflexive.
2860
2861((C)) R US is transitive and symmetric but not reflexive
2862
2863((D)) R US is reflexive and symmetric.
2864
2865 Ans : D
2866
2867
2868((Q65))1_//Define an equivalence relation R on the positive integers A = {2, 3, 4, . . . , 20} by m R n if the largest prime divisor of m is the same as the largest prime divisor of n. The
2869number of equivalence classes of R is
2870 ((A)) 8
2871
2872((B)) 10
2873
2874((C)) 9
2875
2876((D)) 11
2877
2878Ans :A
2879
2880
2881((Q66))2_//Let R = {(a, a), (a, b), (b, b), (a, c), (c, c)} be a partial order relation on∑ = {a, b, c}.Let ≤ be the corresponding lexicographic order on ∑* Which of the following is true?
2882
2883 ((A)) bc≤ba
2884
2885((B)) abbaaacc≤abbaab
2886
2887((C)) abbac≤abb
2888
2889((D)) abbac≤abbab
2890
2891Ans :B
2892
2893
2894
2895((Q67))1_//Consider the divides relation, m | n, on the set A = {2, 3, 4, 5, 6, 7, 8, 9, 10}. The cardinality of the covering relation for this partial order relation (i.e., the number of edges in the Hasse diagram) is
2896
2897((A)) 4
2898((B)) 6
2899((C)) 5
2900((D)) 7
2901 Ans :D
2902
2903((Q68))1_//Consider the divides relation, m | n, on the set A = {2, 3, 4, 5, 6, 7, 8, 9, 10}. Which of the following permutations of A is not a topological sort of this partial order relation?
2904
2905((A)) 7,2,3,6,9,5,4,10,8
2906((B)) 2,3,7,6,9,5,4,10,8
2907((C)) 2,6,3,9,5,7,4,10,8
2908
2909((D)) 3,7,2,9,5,4,10,8,6
2910Ans :C
2911
2912((Q69))1_//Let A = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} and consider the divides relation on A. Let C denote the length of the maximal chain, M the number of maximal elements, and m the number of minimal elements. Which is true?
2913
2914((A)) C = 3, M = 8, m = 6
2915((B)) C= 4, M = 8, m = 6
2916
2917((C)) C = 3, M = 6, m = 6
2918
2919((D)) C = 4, M = 6, m = 4
2920Ans :A
2921
2922((Q70))1_//Which of the following is true regarding forward scheduling? Forward scheduling is the scheduling of
2923((A)) ofthe end items or finished products
2924
2925((B)) jobs as soon as the requirements are known
2926
2927((C)) the start items or component parts
2928
2929((D)) the final operation first beginning with the due date
2930
2931 Ans : B
2932
2933((Q71))1_//A scheduling technique used to achieve optimum, one-to-one matching of tasks and resources is
2934
2935((A)) the assignment method
2936
2937((B))Johnson's rule
2938
2939((C))the CDS Algorithm
2940
2941((D)) the appointment method
2942
2943Ans :A
2944
2945
2946((Q72))1_//Which of the following is an aid used to monitor jobs in process?
2947((A)) a Gantt load chart
2948
2949((B))the assignment method
2950
2951((C))a Gantt schedule chart
2952
2953((D)) Johnson's Rule
2954
2955 Ans :C
2956
2957
2958((Q73))1_//Which of the following dispatching rules allows easy updates?
2959((A)) FCFS: first come, first served
2960
2961((B))SPT: shortest processing time
2962
2963((C))EDD: earliest due date
2964
2965((D)) CR: critical ratio
2966
2967 Ans :D
2968
2969
2970((Q74))1_//In the movie Cheaper by the Dozen," there are 12 children in the family.
2971How many children were born on the same day of the week?
2972
2973((A)) 2
2974
2975((B))3
2976
2977((C))4
2978
2979((D)) 5
2980
2981Ans :A
2982
2983
2984((Q75))1_//There are 14 family members how many family members including mother and father are born in the same month
2985
2986((A)) 2
2987
2988((B))2
2989
2990((C))4
2991
2992((D)) 5
2993
2994 Ans :B
2995
2996((Q76))1_//There are 12 children in the family and 4 children's bedrooms in the house,how many children are sleeping in at least one of them?
2997
2998((A)) 2
2999
3000((B))2
3001
3002((C))3
3003
3004((D)) 5
3005
3006 Ans :C
3007
3008
3009((Q77))1_//Elementary School has 500 students. How many of them were born
3010on the same day of the year.
3011
3012((A)) 2
3013
3014((B))4
3015
3016((C))3
3017
3018((D)) 5
3019
3020Ans :A
3021
3022
3023((Q78))1_//There are 800,000 pine trees in a forest. Each pine tree has no more than 600,000 needles.
3024How many of the trees have the same number of needles.
3025((A)) 5
3026
3027((B))4
3028
3029((C))3
3030
3031((D))2
3032
3033 Ans : D
3034
3035
3036((Q79))1_//There are 50 baskets of apples. Each basket contains no more than 24 apples. How many baskets have the same number of apples.
3037((A)) 5
3038
3039((B))4
3040
3041((C))3
3042
3043((D))2
3044
3045 Ans :C
3046
3047
3048((Q80))1_//Among any 4 numbers one can how many numbers so that their difference is divisible by 3.
3049
3050((A)) 5
3051
3052((B))4
3053
3054((C))3
3055
3056((D))2
3057
3058 Ans :D
3059
3060((Q81))1_//Given n+1 numbers how many numbers are there whose difference is divisible by n .
3061.
3062((A)) 5
3063
3064((B))2
3065
3066((C))3
3067
3068((D))4
3069
3070 Ans :B
3071
3072
3073
3074((Q82))1_//Show that for any natural number n which number composed of digits 5 and 0 only and divisible by n.)
3075
3076((A)) 5 and 0
3077
3078((B))2 and 5
3079
3080((C))3 and 5
3081
3082((D))4 and 5
3083
3084Ans :A
3085
3086
3087
3088((Q83))1_//Given 12 different 2-digit numbers, how many of them should be chossed so that t their
3089difference is a two-digit number with identical first and second digit.
3090
3091
3092((A)) 5
3093
3094((B))2
3095
3096((C))3
3097
3098((D))4
3099
3100 Ans :B
3101
3102
3103
3104((Q84))2_//There are five points inside an equilateral triangle of side length 2.
3105How many of them are the points that are within 1 unit distance from each other.
3106
3107((A)) 5
3108
3109((B))4
3110
3111((C))3
3112
3113((D))2
3114
3115 Ans :D
3116
3117
3118
3119((Q85))2_//There are 10 (possibly overlapping) small line segments marked on a bigger line segment of length 1. If we add up the lengths of the marked segments, we get 1.1. How many of them are marked segments have a common point.
3120((A)) 5
3121
3122((B))4
3123
3124((C))3
3125
3126((D))2
3127
3128 Ans :D
3129
3130
3131
3132((Q86))2_//There are 13 squares of side 1 positioned inside a circle of radius 2. How many squares have a common point.
3133((A)) 5
3134
3135((B))2
3136
3137((C))3
3138
3139((D))4
3140
3141Ans : A
3142
3143
3144
3145((Q87))2_//Show that in any group of n people how many have have the same number of friends
3146
3147((A)) 5
3148
3149((B))2
3150
3151((C))3
3152
3153((D))4
3154
3155Ans : A
3156
3157
3158
3159((Q88))2_//A partial ordered relation is transitive, reflexive and
3160
3161((A)) antisymmetric.
3162
3163((B))bisymmetric
3164
3165((C))antireflexive
3166
3167((D))asymmetric
3168
3169Ans :A
3170
3171
3172
3173((Q89))2_//Let N = {1, 2, 3, ….} be ordered by divisibility, which of the following subset is totally ordered,
3174
3175((A)) 2, 6, 24
3176((B))3, 5, 15
3177((C))2, 9, 16
3178((D))4, 15, 30
3179
3180
3181Ans :A
3182
3183
3184
3185((Q90))1_//Let A = Z+, be the set of positive integers, and R be the relation on A defined by a R b if and only if there exist a k Z+such that a = bk. Which one of the following belongs to R?
3186
3187((A)) (8, 128)
3188
3189((B))(16, 256)
3190
3191((C))(11, 3)
3192
3193((D))(169, 13)
3194
3195Ans :D
3196
3197
3198
3199((Q91))2_//For the sequence defined by the following recurrence relation
3200Tn =nTn-1 ,with initial conditionT1 =7, the explicit formula for Tnis
3201
3202((A)) Tn =n7 n-1
3203
3204((B)) Tn=7.n!
3205
3206((C)) Tn=n!/7
3207
3208((D))Tn=n!-7
3209
3210 Ans :B
3211
3212
3213
3214((Q92))1_//The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
3215
3216((A)) Reflexive
3217
3218((B)) Symmetric
3219
3220((C)) Transitive
3221
3222((D))Asymmetric.
3223
3224 Ans :C
3225
3226
3227
3228((Q93))1_//Pigeonhole principle states that AB and IAI IBI then:
3229((A)) f is not onto
3230
3231((B)) f is not one-one
3232
3233((C)) f is neither one-one nor onto
3234
3235((D))f may be one-one.
3236
3237 Ans : B
3238
3239
3240
3241((Q94))1_//The number of functions from an m element set to an n element set is:
3242
3243((A)) mn
3244
3245((B)) m + n
3246
3247((C)) nm
3248
3249((D))nm
3250
3251 Ans : A
3252
3253
3254
3255((Q95))2_//If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1is
3256
3257((A)) {(3,3), (3,4), (3,5)}
3258((B)) {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}
3259((C)) {(3,3), (3,5), (5,3), (5,5)}
3260((D)){(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}
3261Ans :C
3262
3263
3264((Q96))1_//In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities
3265
3266((A)) 100
3267
3268((B)) 120
3269
3270((C)) 110
3271
3272((D))150
3273
3274 Ans :B
3275
3276
3277
3278((Q97))1_//A debating team consists of 3 boys and 2 girls. Find the number of ways they can sit in a row?
3279 ((A)) 120
3280
3281((B)) 24
3282
3283((C)) 720
3284
3285((D))12
3286
3287 Ans :A
3288
3289
3290((Q98))1_//Find the number of relations from A = {cat, dog, rat} to B = {male , female}
3291 ((A)) 64
3292
3293((B)) 6
3294
3295((C)) 32
3296
3297((D))15
3298
3299Ans : A
3300
3301
3302
3303((Q99))1_//A relation that is reflexive, anti-symmetric and transitive is a
3304
3305((A))Function
3306
3307((B)) Equivalence Relation
3308
3309((C)) Partial Order
3310
3311((D))None of these
3312
3313 Ans :C
3314
3315((Q100))2_//The answer of the recurrence relation will be Tk2 Tk -1, T01.
3316((A))tn=2n
3317
3318((B))tn=n
3319
3320((C)) tn=0
3321
3322((D))tn
3323
3324 Ans :A
3325
3326
3327
3328((Q101))2_//If any five numbers from 1 to 8 are chosen, then
3329How many of them will add upto 9.
3330
3331((A))3
3332
3333((B))5
3334
3335((C)) 2
3336
3337((D))1
3338
3339 Ans :C
3340
3341
3342
3343((Q102))2_//If f is a homomorphism from a commutative semigroup (S, *) onto a semigroupT, *,the it is also
3344
3345((A))transitive
3346
3347((B))Commutative
3348
3349((C)) Associative
3350
3351((D))None of the above
3352
3353 Ans :B
3354
3355
3356
3357
3358((Q103))2_//Find a generating function to count the number of integral solutions to e1+ e2+ e3= 10,iffor each I, 0 iei
3359
3360((A))1/(x-3)2
3361
3362((B))1/(x-2)
3363
3364((C)) 0
3365
3366((D))None of the above
3367
3368 Ans : A
3369
3370
3371
3372((Q104))2_//Let X be the set of all programs of a given programming language. Let R the relation on Xbe defined asP1 R P2 if P1 and P2 give the same output on all the inputs for which they terminate.Is R an equivalence relation?
3373
3374((A))no
3375
3376((B))yes
3377
3378((C)) cant say
3379
3380((D))None of the above
3381
3382 Ans : B
3383
3384
3385
3386
3387((Q105))2_//Let A 1, 2, 4, 8, 16and relation R1 be partial order of divisibility on A. Let
3388A0, 1, 2, 3, 4and R2 be the relation “less than or equal to” on integers. What are A’, R1 and A, R2 are ?
3389
3390((A))posets
3391
3392((B))Isomorphic posets
3393
3394((C)) subsets
3395
3396((D))None of the above
3397
3398 Ans :B
3399
3400
3401
3402
3403((Q106))2_//Solve the following recurrence relation and indicate if it is a linear homogeneous relationornot
3404
3405((A))Linear
3406
3407((B))Linear homogeneous
3408
3409((C)) Linear non homogeneous
3410
3411((D))None of the above
3412
3413 Ans :C
3414
3415
3416
3417((Q107))1_//Find a recurrence relation for the number of ways to arrange flags on a flagpole n feet tallusing 4 types of flags: red flags 2 feet high, white, blue and yellow flags each 1 foot high.
3418
3419((A))10
3420
3421((B))11
3422
3423((C)) 9
3424
3425((D))7
3426
3427 Ans : A
3428
3429
3430
3431((Q108))1_//Find the coefficient of x10 in xx
3432((A))10
3433
3434((B))11
3435
3436((C)) 9
3437
3438((D)) 7
3439
3440 Ans : B
3441
3442
3443
3444((Q109))1_//Can we solve recurrence relation Sk4Sk -13Sk3k.
3445((A))Yes
3446
3447((B))No
3448
3449((C)) Can’t say
3450
3451((D))None of these
3452
3453 Ans: B
3454
3455
3456
3457((Q110))2_//Let R be the relation on the set of ordered pairs of positive integers such that
3458a, b, c, dR if and only if ad = bc. Determine whether R is an equivalence relation ora partial ordering.
3459
3460((A))Equivalence
3461
3462((B))Non equivalence
3463
3464((C)) Can’t say
3465
3466((D))None of these
3467
3468 Ans: A
3469
3470
3471
3472((Q111))2_//What is the minimum number of students required in a class to be sure that at least 6 willreceive the same grade if there are five possible grades A, B,C, D and F?
3473
3474((A))0
3475
3476((B))20
3477
3478((C)) 1
3479
3480((D))26
3481
3482 Ans : D
3483
3484
3485
3486((Q112))2_//Let m be a positive integer with m>1. Determine whether or not the following relation is and equivalent relation.R {a, ba b(mod m)}
3487
3488((A))Equivalence
3489
3490((B))Non equivalence
3491
3492((C)) Can’t say
3493
3494((D))None of these
3495
3496 Ans: A
3497
3498
3499
3500((Q113))2_//Solve for an , the recurrence relationan-2an-1- 3an-2=0, n>= 2, with a0=3 and a1=1 what are coefficient terms?
3501
3502((A))2,1
3503
3504((B))2,3
3505
3506((C)) 1,2
3507
3508((D))2,2
3509
3510 Ans: A
3511
3512
3513((Q114))1_//In a class of 60 boys, 45 boys play cards and 30 boys play carrom. How many boys playboth games? How many play cards only and how many play carrom only?
3514
3515((A))30,15
3516
3517((B))15,30
3518
3519((C)) 15,25
3520
3521((D))25,30
3522
3523 Ans:A
3524
3525
3526
3527((Q115))1_ana_end//Let A 2,-1,0,1,2,B 0,1,4and f : A B is defined as f(x)x2 is a function. If sofind that whether it is one to one or bijection?
3528
3529((A))both
3530
3531((B))only one to one
3532
3533((C)) none of them
3534
3535((D))can’t say
3536
3537 Ans :C
3538
3539
3540((MARKS)) (1/2/3...) 1
3541((QUESTION))116 A={a, b} and B={1, 2, 3}, what is the value of (A cross B) intersection ( B cross A)
3542
3543((OPTION_A)) { a}
3544
3545((OPTION_B)) { b}
3546
3547((OPTION_C)) {1, 2, 3}
3548
3549((OPTION_D)) null set
3550
3551((CORRECT_CHOICE)) (A/B/C/D) D
3552((EXPLANATION)) (OPTIONAL)
3553
3554((MARKS)) (1/2/3...) 1
3555((QUESTION))117 Warshall algorithm can be used to find –
3556
3557((OPTION_A)) Composition
3558((OPTION_B)) Transitive relation
3559((OPTION_C)) Negation
3560((OPTION_D)) poset
3561((CORRECT_CHOICE)) (A/B/C/D) B
3562((EXPLANATI
3563
3564
3565((MARKS)) (1/2/3. 1
3566((QUESTION))118 Equivalence relation must not satisfy --
3567
3568((OPTION_A)) Antisymmetric
3569((OPTION_B)) Reflexive
3570((OPTION_C)) Symmetric
3571((OPTION_D)) Transitive
3572((CORRECT_CHOICE)) (A/B/C/D) A
3573((EXPLANATION)) (OPTIONAL)
3574
3575((MARKS)) (1/2/3...) 1
3576((QUESTION))119 partial order relation is reflexive , transitive and ?
3577
3578((OPTION_A)) antisymmetric
3579
3580((OPTION_B)) symmeric
3581
3582((OPTION_C)) asymmetric
3583
3584((OPTION_D)) none
3585
3586((CORRECT_CHOICE)) (A/B/C/D) A
3587((EXPLANATION)) (OPTIONAL)
3588
3589
3590((MARKS)) (1/2/3...) 1
3591((QUESTION))120 A crossproduct B = B crossproduct A , where A , B is matrix then
3592
3593((OPTION_A)) A is empty
3594
3595((OPTION_B)) B is empty
3596
3597((OPTION_C)) A equal to B
3598
3599((OPTION_D)) none
3600
3601((CORRECT_CHOICE)) (A/B/C/D) C
3602((EXPLANATION)) (OPTIONAL)
3603
3604((MARKS)) (1/2/3...) 1
3605((QUESTION))122 If A= { 1,2,{1,2}} then P(P(A)) has
3606
3607((OPTION_A)) 4 elements
3608
3609((OPTION_B)) 8 elements
3610
3611((OPTION_C)) 256 elements
3612
3613((OPTION_D)) 16 elements
3614
3615((CORRECT_CHOICE)) (A/B/C/D) C
3616((EXPLANATION)) (OPTIONAL)
3617
3618
3619((MARKS)) (1/2/3...) 1
3620((QUESTION))123 if A is set of children in family then relation - " x is brother of y " on set A is ?
3621
3622((OPTION_A)) reflexive
3623
3624((OPTION_B)) symmetric,transitive
3625
3626((OPTION_C)) antisymmetric
3627
3628((OPTION_D)) none
3629
3630((CORRECT_CHOICE)) (A/B/C/D) B
3631((EXPLANATION)) (OPTIONAL)
3632
3633((MARKS)) (1/2/3...) 1
3634((QUESTION))124 The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
3635
3636((OPTION_A)) Reflexive
3637
3638((OPTION_B)) Transitive
3639
3640((OPTION_C)) Symmetric
3641
3642((OPTION_D)) Asymmetric
3643
3644((CORRECT_CHOICE)) (A/B/C/D) B
3645((EXPLANATION)) (OPTIONAL)
3646
3647
3648((MARKS)) (1/2/3...) 1
3649
3650((QUESTION))125 Find the number of relations from A = {cat, dog, rat} to B = {male , female}
3651
3652((OPTION_A)) 64
3653((OPTION_B)) 6
3654((OPTION_C)) 56
3655((OPTION_D)) 128
3656((CORRECT_CHOICE)) (A/B/C/D) A
3657((EXPLANATION)) (OPTIONAL)
3658
3659((MARKS)) (1/2/3...) 1
3660((QUESTION))126 For f: A ->B , the co-domain set is ,
3661
3662((OPTION_A)) A
3663((OPTION_B)) B
3664((OPTION_C)) Both A,B
3665((OPTION_D)) none
3666((CORRECT_CHOICE)) (A/B/C/D) B
3667((EXPLANATION)) (OPTIONAL)
3668
3669
3670((MARKS)) (1/2/3...) 1
3671((QUESTION))127 Which is recurrence relation for fibonacci series ---
3672
3673((OPTION_A)) fn = f(n-2) + f(n-1)
3674((OPTION_B)) fn = f(n-2) - f(n-1)
3675((OPTION_C)) fn = f(n-2) * f(n-1)
3676((OPTION_D)) None
3677((CORRECT_CHOICE)) (A/B/C/D) A
3678((EXPLANATION)) (OPTIONAL)
3679
3680((MARKS)) (1/2/3...) 1
3681((QUESTION))128 If A,B are disjoint sets and (A,B) belongs to relation R then
3682
3683((OPTION_A)) R is symmetric
3684
3685((OPTION_B)) R is reflexive
3686
3687((OPTION_C)) R is transitive
3688
3689((OPTION_D)) antisymmetric
3690
3691((CORRECT_CHOICE)) (A/B/C/D) A
3692((EXPLANATION)) (OPTIONAL)
3693
3694
3695((MARKS)) (1/2/3...) 1
3696((QUESTION))129 If A= { 0,{1,2}, {} } then P(A) has
3697((OPTION_A)) 4 elements
3698((OPTION_B)) 8 elements
3699((OPTION_C)) 256 elements
3700((OPTION_D)) 16 elements
3701((CORRECT_CHOICE)) (A/B/C/D) B
3702((EXPLANATION)) (OPTIONAL)
3703
3704((MARKS)) (1/2/3...) 1
3705((QUESTION))130 If A= { a,b,{a,c},{} } then {a,c} - A = ?
3706((OPTION_A)) {a,b}
3707((OPTION_B)) {b , {a,c}}
3708((OPTION_C)) { c }
3709((OPTION_D)) None
3710((CORRECT_CHOICE)) (A/B/C/D) C
3711((EXPLANATION)) (OPTIONAL)
3712
3713
3714((MARKS)) (1/2/3...) 1
3715((QUESTION))131 if f and g are 2 functions then fog is called as –
3716
3717((OPTION_A)) Inverse
3718((OPTION_B)) Composite
3719((OPTION_C)) recurence
3720((OPTION_D)) None
3721((CORRECT_CHOICE)) (A/B/C/D) B
3722((EXPLANATION)) (OPTIONAL)
3723
3724((MARKS)) (1/2/3...) 1
3725((QUESTION))132 function can’t be
3726
3727((OPTION_A)) One-one
3728((OPTION_B)) Onto
3729((OPTION_C)) One to many
3730((OPTION_D)) Many to one
3731((CORRECT_CHOICE)) (A/B/C/D) C
3732((EXPLANATION)) (OPTIONAL)
3733
3734
3735((MARKS)) (1/2/3...) 2
3736((QUESTION))133 If A={2,3,5,6,10,15,30} and aRb if a|b then (A,R) is
3737((OPTION_A)) Lattice
3738((OPTION_B)) Poset
3739((OPTION_C)) poset having LUB
3740((OPTION_D)) None
3741((CORRECT_CHOICE)) (A/B/C/D) C
3742((EXPLANATION)) (OPTIONAL)
3743
3744
3745((MARKS)) (1/2/3...) 2
3746((QUESTION))134 The number of distinct relations on a set of 3 elements is
3747((OPTION_A)) 8
3748((OPTION_B)) 9
3749((OPTION_C)) 18
3750((OPTION_D)) 512
3751((CORRECT_CHOICE)) (A/B/C/D) D
3752((EXPLANATION)) (OPTIONAL)
3753
3754
3755((MARKS)) (1/2/3...) 2
3756((QUESTION))135 Hasse diagram is used to ,represent ?
3757((OPTION_A)) Poset
3758((OPTION_B)) Subset
3759((OPTION_C)) null set
3760((OPTION_D)) None
3761((CORRECT_CHOICE)) (A/B/C/D) A
3762((EXPLANATION)) (OPTIONAL)
3763
3764
3765
3766
3767
3768((MARKS)) (1/2/3...) 2
3769((QUESTION))136 S={1,2,3….,8,9} find which is valid partition ?
3770((OPTION_A)) Null set
3771((OPTION_B)) {{S}}
3772((OPTION_C)) { null set}
3773((OPTION_D)) None
3774((CORRECT_CHOICE)) (A/B/C/D) B
3775((EXPLANATION)) (OPTIONAL)
3776
3777
3778((MARKS)) (1/2/3...) 2
3779((QUESTION))137 X = {1,2,3,4,5} , A = {{1,2},{3,4,5}} , B = { {1,2,3} ,{4}}
3780((OPTION_A)) both A , B are valid partition
3781((OPTION_B)) both A , B are invalid partition
3782((OPTION_C)) A is valid but B is invalid
3783((OPTION_D)) None
3784((CORRECT_CHOICE)) (A/B/C/D) C
3785((EXPLANATION)) (OPTIONAL)
3786
3787((MARKS)) (1/2/3...) 2
3788((QUESTION))138 S = {(a,b)| a,b are real nos. And 1+ab > 0 } then relation S -
3789((OPTION_A)) Reflexive,symmetric
3790((OPTION_B)) symmetric,transitive
3791((OPTION_C)) Equivalence
3792((OPTION_D)) only transitive
3793((CORRECT_CHOICE)) (A/B/C/D) A
3794((EXPLANATION)) (OPTIONAL)
3795
3796
3797((MARKS)) (1/2/3...) 2
3798((QUESTION))139 R is relation defined on Z as ab> = 0 then R is
3799((OPTION_A)) Equivalence
3800((OPTION_B)) symmetric,transitive
3801((OPTION_C)) Reflexive
3802((OPTION_D)) None
3803((CORRECT_CHOICE)) (A/B/C/D) A
3804((EXPLANATION)) (OPTIONAL)
3805
3806((MARKS)) (1/2/3...) 2
3807((QUESTION))140 Cross product of 2 sets is ,
3808
3809((OPTION_A)) Commutative
3810((OPTION_B)) Associative
3811((OPTION_C)) Distributive
3812((OPTION_D)) None
3813((CORRECT_CHOICE)) (A/B/C/D) D
3814((EXPLANATION)) (OPTIONAL)
3815
3816
3817((MARKS)) (1/2/3...) 2
3818((QUESTION))141 if either set A is empty OR set B is empty, then cross product is,
3819
3820((OPTION_A)) Empty
3821((OPTION_B)) Disjoint
3822((OPTION_C)) Equal
3823((OPTION_D)) None
3824((CORRECT_CHOICE)) (A/B/C/D) A
3825((EXPLANATION)) (OPTIONAL)
3826
3827((MARKS)) (1/2/3...) 1
3828((QUESTION))142 Transitive closure is obtained using
3829
3830((OPTION_A)) Tree
3831((OPTION_B)) Graph
3832((OPTION_C)) Stack
3833((OPTION_D)) Queue
3834((CORRECT_CHOICE)) (A/B/C/D) B
3835((EXPLANATION)) (OPTIONAL)
3836 Q.143) The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
3837• A. Reflexive
3838• B. Transitive
3839• C. Symmetric
3840• D. Asymmetric
3841• ANSWER: B
3842Q.144) Find the number of relations from A = {cat, dog, rat} to B = {male , female}
3843• A. 64
3844• B. 6
3845• C. 32
3846• D. 15
3847• ANSWER: A
3848Q.145) If A={2,3,5,6,10,15,30} and aRb if a|b then (A,R) is
3849• A. lattice
3850• B. poset in which every pair has greatest lower bound
3851• C. poset in which every pair has least upper bound
3852• D. none of these
3853• ANSWER: C
3854Q.146) Let Z denote the set of all integers. Define f : Z —> Z by f(x) = {x / 2 (x is even) 0r (x is odd) then f is
3855A. onto but not one-one
3856B. one-one but not onto
3857C. one-one and onto
3858D. neither one-one nor-onto
3859ANSWER: A
3860Q.147) Partial ordered relation is transitive, reflexive and
3861A. Antisymmetric
3862B. Symmetric
3863C. Anti reflexive.
3864D. Asymmetric
3865ANSWER: A
3866Q.148) The number of distinct relations on a set of 3 elements is
3867A. 8
3868B. 9
3869C. 18
3870D. 512
3871ANSWER: D
3872Q.149) Transitive closure is obtained using
3873 a) stack
3874 b) queue
3875 c) tree
3876 d) graph
3877
3878Q.150) if either set A is empty OR set B is empty, then cross product is,
3879 a) empty
3880 b) disjoint
3881 c) equal
3882 d) none
3883 Q.151) Cross product of 2 sets is ,
3884 a) commutative
3885 b) associative
3886 c) distributive
3887 d) none
3888Q.152) function can’t be –
3889 a) one – one b) onto c) one to many d) many to one
3890Q.153) if f and g are 2 functions then fog is called as –
3891 a) inverse b) composite c) linear d) homogeneous
3892Q.154) out of 25 people , how many will have B’day on same day --
3893 a) 3
3894 b) 2
3895 c) 5
3896 d) 4
3897Q.155) Which is recurrence relation for fibonacci series ---
3898 a) fn = f(n-2) + f(n-1)
3899 b) fn = f(n-2) - f(n-1)
3900 c) fn = f(n-2) * f(n-1)
3901 d) none
3902Q.156) For f: A -> B , the co-domain set is ,
3903 a) A
3904 b) B
3905 c) A,B
3906 d) none
3907Q.157) Equivalence relation must satisfy --
3908 a) reflexive
3909 b) symmetric
3910 c) transitive
3911 d) all a,b,c
3912Q.158) Warshall algorithm can be used to find –
3913 a) transitive closure
3914 b) composition
3915 c) recurrence
3916 d) none
3917Q.159) Hasse diagram used for --
3918 a) poset
3919 b) digraph
3920 c) composition d) recurrence
3921((Q160))1_//The number of functions from an m element set to an n element set is:
3922
3923((A)) mn
3924
3925((B)) m + n
3926
3927((C)) nm
3928
3929((D))nm
3930
3931 Ans : A
3932
3933
3934
3935((Q161))2_//If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1is
3936
3937((A)) {(3,3), (3,4), (3,5)}
3938((B)) {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}
3939((C)) {(3,3), (3,5), (5,3), (5,5)}
3940((D)){(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}
3941Ans :C
3942
3943
3944((Q162))1_//In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities
3945
3946((A)) 100
3947
3948((B)) 120
3949
3950((C)) 110
3951
3952((D))150
3953
3954 Ans :B
3955
3956
3957
3958((Q163))1_//A debating team consists of 3 boys and 2 girls. Find the number of ways they can sit in a row?
3959 ((A)) 120
3960
3961((B)) 24
3962
3963((C)) 720
3964
3965((D))12
3966
3967 Ans :A
3968
3969
3970((Q164))1_//Find the number of relations from A = {cat, dog, rat} to B = {male , female}
3971 ((A)) 64
3972
3973((B)) 6
3974
3975((C)) 32
3976
3977((D))15
3978
3979Ans : A
3980
3981
3982
3983((Q165))1_//A relation that is reflexive, anti-symmetric and transitive is a
3984
3985((A))Function
3986
3987((B)) Equivalence Relation
3988
3989((C)) Partial Order
3990
3991((D))None of these
3992
3993 Ans :C
3994
3995
3996((MARKS)) (1/2/3...) 1
3997((QUESTION))166 A={a, b} and B={1, 2, 3}, what is the value of (A cross B) intersection ( B cross A)
3998
3999((OPTION_A)) { a}
4000
4001((OPTION_B)) { b}
4002
4003((OPTION_C)) {1, 2, 3}
4004
4005((OPTION_D)) null set
4006
4007((CORRECT_CHOICE)) (A/B/C/D) D
4008((EXPLANATION)) (OPTIONAL)
4009
4010((MARKS)) (1/2/3...) 1
4011((QUESTION))167 Warshall algorithm can be used to find –
4012
4013((OPTION_A)) Composition
4014((OPTION_B)) Transitive relation
4015((OPTION_C)) Negation
4016((OPTION_D)) poset
4017((CORRECT_CHOICE)) (A/B/C/D) B
4018((EXPLANATI
4019
4020
4021((MARKS)) (1/2/3...) 1
4022((QUESTION))168 Equivalence relation must not satisfy --
4023
4024((OPTION_A)) Antisymmetric
4025((OPTION_B)) Reflexive
4026((OPTION_C)) Symmetric
4027((OPTION_D)) Transitive
4028((CORRECT_CHOICE)) (A/B/C/D) A
4029((EXPLANATION)) (OPTIONAL)
4030
4031((MARKS)) (1/2/3...) 1
4032((QUESTION))169 partial order relation is reflexive , transitive and ?
4033
4034((OPTION_A)) antisymmetric
4035
4036((OPTION_B)) symmeric
4037
4038((OPTION_C)) asymmetric
4039
4040((OPTION_D)) none
4041
4042((CORRECT_CHOICE)) (A/B/C/D) A
4043((EXPLANATION)) (OPTIONAL)
4044
4045
4046((MARKS)) (1/2/3...) 1
4047((QUESTION))170 A crossproduct B = B crossproduct A , where A , B is matrix then
4048
4049((OPTION_A)) A is empty
4050
4051((OPTION_B)) B is empty
4052
4053((OPTION_C)) A equal to B
4054
4055((OPTION_D)) none
4056
4057((CORRECT_CHOICE)) (A/B/C/D) C
4058((EXPLANATION)) (OPTIONAL)
4059
4060((MARKS)) (1/2/3...) 1
4061((QUESTION))171 If A= { 1,2,{1,2}} then P(P(A)) has
4062
4063((OPTION_A)) 4 elements
4064
4065((OPTION_B)) 8 elements
4066
4067((OPTION_C)) 256 elements
4068
4069((OPTION_D)) 16 elements
4070
4071((CORRECT_CHOICE)) (A/B/C/D) C
4072((EXPLANATION)) (OPTIONAL)
4073
4074
4075((MARKS)) (1/2/3...) 1
4076((QUESTION))172 if A is set of children in family then relation - " x is brother of y " on set A is ?
4077
4078((OPTION_A)) reflexive
4079
4080((OPTION_B)) symmetric,transitive
4081
4082((OPTION_C)) antisymmetric
4083
4084((OPTION_D)) none
4085
4086((CORRECT_CHOICE)) (A/B/C/D) B
4087((EXPLANATION)) (OPTIONAL)
4088
4089((MARKS)) (1/2/3...) 1
4090((QUESTION))173 The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
4091
4092((OPTION_A)) Reflexive
4093
4094((OPTION_B)) Transitive
4095
4096((OPTION_C)) Symmetric
4097
4098((OPTION_D)) Asymmetric
4099
4100((CORRECT_CHOICE)) (A/B/C/D) B
4101((EXPLANATION)) (OPTIONAL)
4102
4103
4104((MARKS)) (1/2/3...) 1
4105
4106((QUESTION))174 Find the number of relations from A = {cat, dog, rat} to B = {male , female}
4107
4108((OPTION_A)) 64
4109((OPTION_B)) 6
4110((OPTION_C)) 56
4111((OPTION_D)) 128
4112((CORRECT_CHOICE)) (A/B/C/D) A
4113((EXPLANATION)) (OPTIONAL)
4114
4115((MARKS)) (1/2/3...) 1
4116((QUESTION))175 For f: A ->B , the co-domain set is ,
4117
4118((OPTION_A)) A
4119((OPTION_B)) B
4120((OPTION_C)) Both A,B
4121((OPTION_D)) none
4122((CORRECT_CHOICE)) (A/B/C/D) B
4123((EXPLANATION)) (OPTIONAL)
4124
4125
4126((MARKS)) (1/2/3...) 1
4127((QUESTION))176 Which is recurrence relation for fibonacci series ---
4128
4129((OPTION_A)) fn = f(n-2) + f(n-1)
4130((OPTION_B)) fn = f(n-2) - f(n-1)
4131((OPTION_C)) fn = f(n-2) * f(n-1)
4132((OPTION_D)) None
4133((CORRECT_CHOICE)) (A/B/C/D) A
4134((EXPLANATION)) (OPTIONAL)
4135
4136((MARKS)) (1/2/3...) 1
4137((QUESTION))177 If A,B are disjoint sets and (A,B) belongs to relation R then
4138
4139((OPTION_A)) R is symmetric
4140
4141((OPTION_B)) R is reflexive
4142
4143((OPTION_C)) R is transitive
4144
4145((OPTION_D)) antisymmetric
4146
4147((CORRECT_CHOICE)) (A/B/C/D) A
4148((EXPLANATION)) (OPTIONAL)
4149
4150
4151((MARKS)) (1/2/3...) 1
4152((QUESTION))178 If A= { 0,{1,2}, {} } then P(A) has
4153((OPTION_A)) 4 elements
4154((OPTION_B)) 8 elements
4155((OPTION_C)) 256 elements
4156((OPTION_D)) 16 elements
4157((CORRECT_CHOICE)) (A/B/C/D) B
4158((EXPLANATION)) (OPTIONAL)
4159
4160((MARKS)) (1/2/3...) 1
4161((QUESTION))179 If A= { a,b,{a,c},{} } then {a,c} - A = ?
4162((OPTION_A)) {a,b}
4163((OPTION_B)) {b , {a,c}}
4164((OPTION_C)) { c }
4165((OPTION_D)) None
4166((CORRECT_CHOICE)) (A/B/C/D) C
4167((EXPLANATION)) (OPTIONAL)
4168
4169
4170((MARKS)) (1/2/3...) 1
4171((QUESTION))180 if f and g are 2 functions then fog is called as –
4172
4173((OPTION_A)) Inverse
4174((OPTION_B)) Composite
4175((OPTION_C)) recurence
4176((OPTION_D)) None
4177((CORRECT_CHOICE)) (A/B/C/D) B
4178((EXPLANATION)) (OPTIONAL)
4179
4180((MARKS)) (1/2/3...) 1
4181((QUESTION))181 function can’t be
4182
4183((OPTION_A)) One-one
4184((OPTION_B)) Onto
4185((OPTION_C)) One to many
4186((OPTION_D)) Many to one
4187((CORRECT_CHOICE)) (A/B/C/D) C
4188((EXPLANATION)) (OPTIONAL)
4189
4190
4191((MARKS)) (1/2/3...) 2
4192((QUESTION))182 If A={2,3,5,6,10,15,30} and aRb if a|b then (A,R) is
4193((OPTION_A)) Lattice
4194((OPTION_B)) Poset
4195((OPTION_C)) poset having LUB
4196((OPTION_D)) None
4197((CORRECT_CHOICE)) (A/B/C/D) C
4198((EXPLANATION)) (OPTIONAL)
4199
4200
4201((MARKS)) (1/2/3...) 2
4202((QUESTION))183 The number of distinct relations on a set of 3 elements is
4203((OPTION_A)) 8
4204((OPTION_B)) 9
4205((OPTION_C)) 18
4206((OPTION_D)) 512
4207((CORRECT_CHOICE)) (A/B/C/D) D
4208((EXPLANATION)) (OPTIONAL)
4209
4210
4211((MARKS)) (1/2/3...) 2
4212((QUESTION))184 Hasse diagram is used to ,represent ?
4213((OPTION_A)) Poset
4214((OPTION_B)) Subset
4215((OPTION_C)) null set
4216((OPTION_D)) None
4217((CORRECT_CHOICE)) (A/B/C/D) A
4218((EXPLANATION)) (OPTIONAL)
4219
4220
4221
4222
4223
4224((MARKS)) (1/2/3...) 2
4225((QUESTION))185 S={1,2,3….,8,9} find which is valid partition ?
4226((OPTION_A)) Null set
4227((OPTION_B)) {{S}}
4228((OPTION_C)) { null set}
4229((OPTION_D)) None
4230((CORRECT_CHOICE)) (A/B/C/D) B
4231((EXPLANATION)) (OPTIONAL)
4232
4233
4234((MARKS)) (1/2/3...) 2
4235((QUESTION))186 X = {1,2,3,4,5} , A = {{1,2},{3,4,5}} , B = { {1,2,3} ,{4}}
4236((OPTION_A)) both A , B are valid partition
4237((OPTION_B)) both A , B are invalid partition
4238((OPTION_C)) A is valid but B is invalid
4239((OPTION_D)) None
4240((CORRECT_CHOICE)) (A/B/C/D) C
4241((EXPLANATION)) (OPTIONAL)
4242
4243((MARKS)) (1/2/3...) 2
4244((QUESTION))187 S = {(a,b)| a,b are real nos. And 1+ab > 0 } then relation S -
4245((OPTION_A)) Reflexive,symmetric
4246((OPTION_B)) symmetric,transitive
4247((OPTION_C)) Equivalence
4248((OPTION_D)) only transitive
4249((CORRECT_CHOICE)) (A/B/C/D) A
4250((EXPLANATION)) (OPTIONAL)
4251
4252
4253((MARKS)) (1/2/3...) 2
4254((QUESTION))188 R is relation defined on Z as ab> = 0 then R is
4255((OPTION_A)) Equivalence
4256((OPTION_B)) symmetric,transitive
4257((OPTION_C)) Reflexive
4258((OPTION_D)) None
4259((CORRECT_CHOICE)) (A/B/C/D) A
4260((EXPLANATION)) (OPTIONAL)
4261
4262((MARKS)) (1/2/3...) 2
4263((QUESTION))189 Cross product of 2 sets is ,
4264
4265((OPTION_A)) Commutative
4266((OPTION_B)) Associative
4267((OPTION_C)) Distributive
4268((OPTION_D)) None
4269((CORRECT_CHOICE)) (A/B/C/D) D
4270((EXPLANATION)) (OPTIONAL)
4271
4272
4273((MARKS)) (1/2/3...) 2
4274((QUESTION))190 if either set A is empty OR set B is empty, then cross product is,
4275
4276((OPTION_A)) Empty
4277((OPTION_B)) Disjoint
4278((OPTION_C)) Equal
4279((OPTION_D)) None
4280((CORRECT_CHOICE)) (A/B/C/D) A
4281((EXPLANATION)) (OPTIONAL)
4282
4283((MARKS)) (1/2/3...) 1
4284((QUESTION))191 Transitive closure is obtained using
4285
4286((OPTION_A)) Tree
4287((OPTION_B)) Graph
4288((OPTION_C)) Stack
4289((OPTION_D)) Queue
4290((CORRECT_CHOICE)) (A/B/C/D) B
4291
4292
4293((MARKS)) (1/2/3...) 1
4294((QUESTION)) Which of the following statement is the negation of the statement,
4295“2 is even and –3 is negative”?
4296((OPTION_A)) 2 is even and –3 is not negative.
4297((OPTION_B)) 2 is odd and –3 is not negative.
4298((OPTION_C)) 2 is even or –3 is not negative.
4299((OPTION_D)) 2 is odd or –3 is not negative.
4300((CORRECT_CHOICE)) (A/B/C/D) D
4301((EXPLANATION)) (OPTIONAL) P: 2 is even. Q:–3 is negative
4302~(P ^ Q)=~P or ~Q
4303
4304((MARKS)) (1/2/3...) 1
4305((QUESTION)) If A × B = B × A , (where A and B are general matrices) then
4306((OPTION_A)) A = φ .
4307((OPTION_B)) A = B’
4308((OPTION_C)) B = A.
4309((OPTION_D)) A’ = B.
4310((CORRECT_CHOICE)) (A/B/C/D) C
4311((EXPLANATION)) (OPTIONAL)
4312
4313
4314((MARKS)) (1/2/3...) 1
4315((QUESTION)) A partial ordered relation is transitive, reflexive and
4316((OPTION_A)) antisymmetric.
4317((OPTION_B)) bisymmetric.
4318((OPTION_C)) antireflexive.
4319((OPTION_D)) asymmetric.
4320((CORRECT_CHOICE)) (A/B/C/D) A
4321((EXPLANATION)) (OPTIONAL)
4322
4323((MARKS)) (1/2/3...) 1
4324((QUESTION)) Let N = {1, 2, 3, ....} be ordered by divisibility, which of the following subset is tot
4325ordered,
4326((OPTION_A)) ( 2 , 6 , 24 ) .
4327((OPTION_B)) ( 3 , 5 , 15 ) .
4328((OPTION_C)) ( 2 , 9 , 16 ) .
4329((OPTION_D)) ( 4 , 15 , 30 ) .
4330((CORRECT_CHOICE)) (A/B/C/D) A
4331((EXPLANATION)) (OPTIONAL) In (2,6,24), every element is divisible by its prev element. 6 dis divisible by 2.24 divisible by 6.
4332In (3,5,15), 5 is not divisible by 3.
4333
4334
4335((MARKS)) (1/2/3...) 1
4336((QUESTION)) If f ( x ) = cos x and g ( x ) = x 3 , then ( fog ) ( x ) is
4337((OPTION_A)) ( cos x ) .
4338((OPTION_B)) cos 3 x.
4339((OPTION_C)) x ( cos x ) .
4340((OPTION_D)) cos x 3 .
4341((CORRECT_CHOICE)) (A/B/C/D) D
4342((EXPLANATION)) (OPTIONAL)
4343
4344((MARKS)) (1/2/3...) 1
4345((QUESTION)) p → q is logically equivalent to
4346((OPTION_A)) ~ q → p
4347((OPTION_B)) ~ p → q
4348((OPTION_C)) ~ p ∧ q
4349((OPTION_D)) ~ p ∨ q
4350((CORRECT_CHOICE)) (A/B/C/D) D
4351((EXPLANATION)) (OPTIONAL)
4352
4353
4354((MARKS)) (1/2/3...) 1
4355((QUESTION)) [ ~ q ∧ ( p → q ) ] → ~ p is,
4356((OPTION_A)) Satisfiable.
4357((OPTION_B)) Unsatisfiable.
4358((OPTION_C)) Tautology.
4359((OPTION_D)) Invalid.
4360((CORRECT_CHOICE)) (A/B/C/D) C
4361((EXPLANATION)) (OPTIONAL)
4362
4363((MARKS)) (1/2/3...) 1
4364((QUESTION)) For a relation R on set A, let M R = m ij , m ij = 1 if a i Ra j and 0 otherwise, be the
4365relation R. If ( M R ) 2 = M R then R is,
4366((OPTION_A)) Symmetric
4367((OPTION_B)) Transitive
4368((OPTION_C)) Antisymmetric
4369((OPTION_D)) Reflexive
4370((CORRECT_CHOICE)) (A/B/C/D) B
4371((EXPLANATION)) (OPTIONAL)
4372
4373
4374((MARKS)) (1/2/3...) 1
4375((QUESTION)) In an examination there are 15 questions of type True or False. How many sequences of answers are possible.
4376((OPTION_A)) 32768
4377((OPTION_B)) 32769
4378((OPTION_C)) 32767
4379((OPTION_D)) 32766
4380((CORRECT_CHOICE)) (A/B/C/D) A
4381((EXPLANATION)) (OPTIONAL) All possible values are 2^15
4382
4383((MARKS)) (1/2/3...) 1
4384((QUESTION)) Find the truth value ( P ∧ Q ) ∧ ~ ( P ∨ Q ) .
4385((OPTION_A)) Tautology
4386((OPTION_B)) Contradiction
4387((OPTION_C)) Contigency
4388((OPTION_D)) Both a and b
4389((CORRECT_CHOICE)) (A/B/C/D) B
4390((EXPLANATION)) (OPTIONAL)
4391
4392
4393((MARKS)) (1/2/3...) 1
4394((QUESTION)) In a survey of 85 people it is found that 31 like to drink milk, 43 like coffee and 39 like tea.
4395Also 13 like both milk and tea, 15 like milk and coffee, 20 like tea and coffee and 12 like none
4396of the three drinks. Find the number of people who like all the three drinks.
4397((OPTION_A)) 8
4398((OPTION_B)) 6
4399((OPTION_C)) 7
4400((OPTION_D)) 9
4401((CORRECT_CHOICE)) (A/B/C/D) A
4402((EXPLANATION)) (OPTIONAL) Let A, B and C is set of people who like to drink milk, take coffee and take tea
4403respectively. Thus |A| = 31, |B| = 43, |C| = 39, |A∩B| = 15, |A∩C| = 13, |B∩C| = 20, |A∪B∪C|
4404= 85 – 12 = 73. Therefore, |A∩B∩C| = 73 + (15 + 13 + 20) – (31 + 43 + 39) = 8.
4405
4406((MARKS)) (1/2/3...) 1
4407((QUESTION)) Consider the set A = {2, 7, 14, 28, 56, 84} and the relation a ≤ b if and only if a
4408Which are part of Hasse diagram for the poset (A, ≤ ) ?
4409((OPTION_A)) (2,2), (2, 14), (2, 28), (2, 56)
4410((OPTION_B)) (28, 28), (28, 56)
4411((OPTION_C)) (56,28)
4412((OPTION_D)) Both A and B
4413((CORRECT_CHOICE)) (A/B/C/D) D
4414((EXPLANATION)) (OPTIONAL) The relation is given by the set {(2,2), (2, 14), (2, 28), (2, 56), (2, 84), (7, 7), (7, 14), (7,
441528), (7, 56), (7, 84), (14, 14), (14, 28), (14, 56), (14, 84), (28, 28), (28, 56), (28, 84), (56, 56),(84, 84)}
4416
4417
4418((MARKS)) (1/2/3...) 2
4419((QUESTION))
4420
4421
4422
4423
4424The Shaded region is described by,
4425((OPTION_A)) C ∪ ( A ∩ B )
4426((OPTION_B)) ( C − ( ( A ∩ C ) ∪ ( C ∩ B ) ) ) ∪ ( A ∩ B )
4427((OPTION_C)) ( C − ( A ∩ C ) ∪ ( C ∩ B ) ) ∪ ( A ∩ B )
4428((OPTION_D)) A ∪ B ∪ C − ( C ∪ ( A ∩ B ) )
4429((CORRECT_CHOICE)) (A/B/C/D) B
4430((EXPLANATION)) (OPTIONAL)
4431
4432((MARKS)) (1/2/3...) 1
4433((QUESTION)) The statement ( p∧q) ⇒ p is a
4434((OPTION_A)) Contingency.
4435((OPTION_B)) Absurdity
4436((OPTION_C)) Tautology
4437((OPTION_D)) None
4438((CORRECT_CHOICE)) (A/B/C/D) C
4439((EXPLANATION)) (OPTIONAL)
4440
4441
4442((MARKS)) (1/2/3...) 1
4443((QUESTION)) Which of the following set is null set?
4444((OPTION_A)) { 0 }
4445((OPTION_B)) { }
4446((OPTION_C)) { φ }
4447((OPTION_D)) φ
4448((CORRECT_CHOICE)) (A/B/C/D) B
4449((EXPLANATION)) (OPTIONAL)
4450
4451((MARKS)) (1/2/3...) 1
4452((QUESTION)) Let P(S) denotes the powerset of set S. Which of the following is always true?
4453((OPTION_A)) P ( P ( S )) = P ( S )
4454((OPTION_B)) P ( S ) I S = P ( S )
4455((OPTION_C)) P ( S ) I P ( P ( S )) = { ∅ }
4456((OPTION_D)) S ∈ P ( S )
4457((CORRECT_CHOICE)) (A/B/C/D) D
4458((EXPLANATION)) (OPTIONAL)
4459
4460
4461((MARKS)) (1/2/3...) 1
4462((QUESTION)) Which of the following represents the set A = {11, 13, 15, 17, 19}?
4463((OPTION_A)) A = { x:x is a natural number greater than 11}
4464((OPTION_B)) A = { x:x is an odd number greater than 11}
4465((OPTION_C)) A = { x:x is a odd number between 10 to 20}
4466((OPTION_D)) A = { x:x is a natural number less than 20}
4467((CORRECT_CHOICE)) (A/B/C/D) C
4468((EXPLANATION)) (OPTIONAL)
4469
4470((MARKS)) (1/2/3...) 1
4471((QUESTION)) Which of the following represents the statement
4472“The number 5 is not a member of the set A”?
4473((OPTION_A)) 5 ∈ A
4474((OPTION_B)) 5 ∉ A
4475((OPTION_C)) A ∉ 5
4476((OPTION_D)) A ∈ 5
4477((CORRECT_CHOICE)) (A/B/C/D) B
4478((EXPLANATION)) (OPTIONAL)
4479
4480
4481((MARKS)) (1/2/3...) 1
4482((QUESTION)) Which of the following represents the set A = { 1, 4, 9, 16, 25}
4483((OPTION_A)) A = { x:x is a square of natural number and less than 5}
4484((OPTION_B)) A = { x:x is an odd natural number less than 30}
4485((OPTION_C)) A = { x:x is an odd natural number between 1 to 30}
4486((OPTION_D)) A = { x:x is a natural number less than 30}
4487((CORRECT_CHOICE)) (A/B/C/D) A
4488((EXPLANATION)) (OPTIONAL)
4489
4490((MARKS)) (1/2/3...) 1
4491((QUESTION)) Which of the following represents the set B = { x : x is
4492an interger, x2 + 1 = 10}?
4493((OPTION_A)) B = { 3 }
4494((OPTION_B)) B = { -3, 3 }
4495((OPTION_C)) B = { }
4496((OPTION_D)) B = { -3, …, 3}
4497((CORRECT_CHOICE)) (A/B/C/D) B
4498((EXPLANATION)) (OPTIONAL)
4499
4500
4501((MARKS)) (1/2/3...) 1
4502((QUESTION)) Which of the following represents the set A = { a, e, i, o, u}?
4503((OPTION_A)) A = { x:x is a alphabet}
4504((OPTION_B)) A = { x:x is English alphabet}
4505((OPTION_C)) A = {x:x is an English alphabet and a vowel}
4506((OPTION_D)) A = {x:x is an English alphabet and a consonant}
4507((CORRECT_CHOICE)) (A/B/C/D) C
4508((EXPLANATION)) (OPTIONAL)
4509
4510((MARKS)) (1/2/3...) 1
4511((QUESTION)) Which of the following is a null ( or empty) set?
4512((OPTION_A)) { x:x is a natural number and x2 + 1 = 10 }
4513((OPTION_B)) { x:x is a natural number and x2 = 121 }
4514((OPTION_C)) { x:x is a natural number and x2 = – 10 }
4515((OPTION_D)) { x:x is a natural number and x2 ≤ 100 }
4516((CORRECT_CHOICE)) (A/B/C/D) C
4517((EXPLANATION)) (OPTIONAL)
4518
4519
4520((MARKS)) (1/2/3...) 1
4521((QUESTION)) Which of the following is a singleton set?
4522((OPTION_A)) { x:x is an integer and x2 = 16 }
4523((OPTION_B)) { x:x is an integer and x2 – 1 = 120 }
4524((OPTION_C)) { x:x is an integer and x2 = x }
4525((OPTION_D)) { x:x is an integer and 4x = 8 }
4526((CORRECT_CHOICE)) (A/B/C/D) D
4527((EXPLANATION)) (OPTIONAL)
4528
4529((MARKS)) (1/2/3...) 1
4530((QUESTION)) If A = { 1,2,3,4,5} and B = { 2,4,5}, then which of the following holds?
4531((OPTION_A)) A ⊂ B
4532((OPTION_B)) B ⊂ A
4533((OPTION_C)) A = B
4534((OPTION_D)) A = Bc
4535((CORRECT_CHOICE)) (A/B/C/D) B
4536((EXPLANATION)) (OPTIONAL)
4537
4538
4539((MARKS)) (1/2/3...) 1
4540((QUESTION)) Which of the following sets is a finite set?
4541((OPTION_A)) { x:x is an integer and x2 > 0}
4542((OPTION_B)) A = { x:x is a prime number greater then 10}
4543((OPTION_C)) {x:x is an integer and x2 = x}
4544((OPTION_D)) A = {x:x is an integer less than 20}
4545((CORRECT_CHOICE)) (A/B/C/D) D
4546((EXPLANATION)) (OPTIONAL)
4547
4548((MARKS)) (1/2/3...) 1
4549((QUESTION)) Which of the following is true for the standard sets?
4550((OPTION_A)) R ⊂ Z
4551((OPTION_B)) Z ⊂ Q
4552((OPTION_C)) Z ⊂ N
4553((OPTION_D)) Q ⊂ N
4554((CORRECT_CHOICE)) (A/B/C/D) C
4555((EXPLANATION)) (OPTIONAL)
4556
4557
4558((MARKS)) (1/2/3...) 1
4559((QUESTION)) If we are dealing with the set of all computer
4560programmers in the world, then which of the following
4561 be a Universal set ?
4562((OPTION_A)) set of all men in the world
4563((OPTION_B)) set of all women in the world
4564((OPTION_C)) set of all people in the world
4565((OPTION_D)) set of all Indians in the world
4566((CORRECT_CHOICE)) (A/B/C/D) C
4567((EXPLANATION)) (OPTIONAL)
4568
4569((MARKS)) (1/2/3...) 1
4570((QUESTION)) If A = {1,3,9} then which of the following is power set of A?
4571((OPTION_A)) { {1,3}, {3,9}, {3,1}. {9,3}, {1,9} }
4572((OPTION_B)) { { }, {1}, {3}, {9}, {1,3}, {1,9}, {3,9}, {1,3,9}}
4573((OPTION_C)) { Ø, {1,4}, {1,9}, {3,7}, A }
4574((OPTION_D)) B = { {1,3}, {3,9} }
4575((CORRECT_CHOICE)) (A/B/C/D) B
4576((EXPLANATION)) (OPTIONAL)
4577
4578
4579((MARKS)) (1/2/3...) 1
4580((QUESTION)) (A’)’ = ?
4581
4582((OPTION_A)) A
4583((OPTION_B)) U-A
4584((OPTION_C)) U
4585((OPTION_D)) A’
4586((CORRECT_CHOICE)) (A/B/C/D) A
4587((EXPLANATION)) (OPTIONAL)
4588
4589((MARKS)) (1/2/3...) 1
4590((QUESTION)) A B is read as ?
4591
4592((OPTION_A)) A is less than B
4593((OPTION_B)) A is a proper subset of B
4594((OPTION_C)) A is a subset of B
4595((OPTION_D)) B is a subset of A
4596((CORRECT_CHOICE)) (A/B/C/D) B
4597((EXPLANATION)) (OPTIONAL)
4598
4599
4600((MARKS)) (1/2/3...) 1
4601((QUESTION)) The intersection of sets A and B is expressed as ?
4602
4603((OPTION_A)) A/B
4604((OPTION_B)) AxB
4605((OPTION_C)) A-B
4606((OPTION_D)) AnB
4607((CORRECT_CHOICE)) (A/B/C/D) D
4608((EXPLANATION)) (OPTIONAL)
4609
4610((MARKS)) (1/2/3...) 1
4611((QUESTION)) A’ will contain how many elements from
4612 the original set A
4613
4614((OPTION_A)) 0
4615((OPTION_B)) 1
4616((OPTION_C)) Infinite
4617((OPTION_D)) All elements in A
4618((CORRECT_CHOICE)) (A/B/C/D) A
4619((EXPLANATION)) (OPTIONAL)
4620
4621
4622((MARKS)) (1/2/3...) 1
4623((QUESTION)) Empty set is a ?
4624
4625((OPTION_A)) Invalid Set
4626((OPTION_B)) Infinite Set
4627((OPTION_C)) Finite Set
4628((OPTION_D)) None of the above
4629((CORRECT_CHOICE)) (A/B/C/D) C
4630((EXPLANATION)) (OPTIONAL)
4631
4632((MARKS)) (1/2/3...) 1
4633((QUESTION)) How many rational and irrational numbers are possible
4634between 0 and 1 ?
4635
4636((OPTION_A)) 0
4637((OPTION_B)) 1
4638((OPTION_C)) Finite
4639((OPTION_D)) Infinite
4640((CORRECT_CHOICE)) (A/B/C/D) D
4641((EXPLANATION)) (OPTIONAL) rational and irrational numbers between 0& 1 are
46420.1,0.2,0.3,0.12,0.23,0.123..........
4643
4644
4645((MARKS)) (1/2/3...) 1
4646((QUESTION)) Every set is a ___________ of itself
4647
4648((OPTION_A)) Subset
4649((OPTION_B)) Compliment
4650((OPTION_C)) Difference
4651((OPTION_D)) Cartesian Product
4652((CORRECT_CHOICE)) (A/B/C/D) A
4653((EXPLANATION)) (OPTIONAL)
4654
4655((MARKS)) (1/2/3...) 1
4656((QUESTION)) If A =[5,6,7] and B=[7,8,9]then A U B is equal to:
4657
4658((OPTION_A)) [5,6,7]
4659((OPTION_B)) [5,6,7,8,9]
4660((OPTION_C)) [7,8,9]
4661((OPTION_D)) None of these
4662((CORRECT_CHOICE)) (A/B/C/D) B
4663((EXPLANATION)) (OPTIONAL)
4664
4665
4666((MARKS)) (1/2/3...) 1
4667((QUESTION)) If A has m elements and B has n elements, then A x B has elements ?
4668
4669((OPTION_A)) m + n
4670((OPTION_B)) m - n
4671((OPTION_C)) m x n
4672((OPTION_D)) 2n
4673((CORRECT_CHOICE)) (A/B/C/D) C
4674((EXPLANATION)) (OPTIONAL)
4675
4676((MARKS)) (1/2/3...) 1
4677((QUESTION)) A — B will contain elements in ?
4678
4679((OPTION_A)) Neither A nor B
4680((OPTION_B)) B not in A
4681((OPTION_C)) A not in B
4682((OPTION_D)) Both A and B
4683((CORRECT_CHOICE)) (A/B/C/D) C
4684((EXPLANATION)) (OPTIONAL)
4685
4686
4687((MARKS)) (1/2/3...) 1
4688((QUESTION)) A—B is read as ?
4689
4690((OPTION_A)) Difference of A and B
4691((OPTION_B)) Difference of B and A
4692((OPTION_C)) None of the above
4693((OPTION_D)) Both a and b
4694((CORRECT_CHOICE)) (A/B/C/D) A
4695((EXPLANATION)) (OPTIONAL)
4696
4697((MARKS)) (1/2/3...) 1
4698((QUESTION)) The union of sets A and B is
4699((OPTION_A)) A/B
4700((OPTION_B)) AUB
4701((OPTION_C)) AxB
4702((OPTION_D)) A-B
4703((CORRECT_CHOICE)) (A/B/C/D) B
4704((EXPLANATION)) (OPTIONAL)
4705
4706
4707((MARKS)) (1/2/3...) 1
4708((QUESTION)) If R = {(1,1),(2,3),(4,5)}, then
4709range of the function is ?
4710
4711((OPTION_A)) Range R = {I,3,5}
4712((OPTION_B)) Range R {1,2,5}
4713((OPTION_C)) Range R = {2,3,4,5}
4714((OPTION_D)) Range R {1,1,4,5}
4715((CORRECT_CHOICE)) (A/B/C/D) A
4716((EXPLANATION)) (OPTIONAL)
4717
4718((MARKS)) (1/2/3...) 2
4719((QUESTION)) The set of intelligent students in a class is.
4720((OPTION_A)) A null set
4721((OPTION_B)) A finite set
4722((OPTION_C)) A singleton set
4723((OPTION_D)) Not a well defined collection
4724((CORRECT_CHOICE)) (A/B/C/D) D
4725((EXPLANATION)) (OPTIONAL) Not a well defined collection, Since, intelligency is not defined for students in a class i.e., Not a well defined collection.
4726
4727
4728((MARKS)) (1/2/3...) 1
4729((QUESTION)) If A is any set, then
4730((OPTION_A)) A ∪ A' = ø
4731((OPTION_B)) A ∩ A' = U
4732((OPTION_C)) A ∪ A' = U
4733
4734((OPTION_D)) None of these
4735((CORRECT_CHOICE)) (A/B/C/D) C
4736((EXPLANATION)) (OPTIONAL)
4737
4738((MARKS)) (1/2/3...) 1
4739((QUESTION)) The number of proper subsets of the set {1, 2, 3} is.
4740((OPTION_A)) 8
4741((OPTION_B)) 6
4742((OPTION_C)) 7
4743((OPTION_D)) 5
4744((CORRECT_CHOICE)) (A/B/C/D) B
4745((EXPLANATION)) (OPTIONAL) Number of proper subsets of the set {1, 2, 3) = 2³ - 2 = 6.
4746
4747
4748((MARKS)) (1/2/3...) 1
4749((QUESTION)) A = {x: x ≠ x }represents.
4750((OPTION_A)) {0}
4751((OPTION_B)) {1}
4752((OPTION_C)) {}
4753
4754((OPTION_D)) {x}
4755((CORRECT_CHOICE)) (A/B/C/D) C
4756((EXPLANATION)) (OPTIONAL)
4757
4758((MARKS)) (1/2/3...) 2
4759((QUESTION)) If A and B are any two sets, then A ∪ (A ∩ B) is equal to.
4760((OPTION_A)) A
4761((OPTION_B)) B
4762((OPTION_C)) Ac
4763((OPTION_D)) Bc
4764((CORRECT_CHOICE)) (A/B/C/D) A
4765((EXPLANATION)) (OPTIONAL) A ∩ B ⊆ A Hence A ∪ (A ∩ B) = A
4766
4767
4768((MARKS)) (1/2/3...) 1
4769((QUESTION)) Which of the following is a subset of {b, c, d}?
4770((OPTION_A)) { }
4771((OPTION_B)) {a}
4772((OPTION_C)) {1 , 2 , 3}
4773((OPTION_D)) {a, b, c}
4774((CORRECT_CHOICE)) (A/B/C/D) A
4775((EXPLANATION)) (OPTIONAL) The null set, { }, is a subset of every set. A subset of {b, c, d} is { }.
4776
4777((MARKS)) (1/2/3...) 1
4778((QUESTION)) How many subsets does the set {a, b, c, d, e} have?
4779((OPTION_A)) 2
4780((OPTION_B)) 5
4781((OPTION_C)) 10
4782((OPTION_D)) 32
4783((CORRECT_CHOICE)) (A/B/C/D) D
4784((EXPLANATION)) (OPTIONAL) The number of subsets in a set of n members is 2n. For {a, b, c, d, e}, n = 5 => number of subsets = 25 = 32
4785
4786
4787((MARKS)) (1/2/3...) 1
4788((QUESTION)) Which of the following represents numbers greater than -3 but less than 6 ?
4789((OPTION_A)) {x : -3 > x > 6}
4790((OPTION_B)) {x: -3 ≥ x ≥ 6}
4791((OPTION_C)) {x: -3 < x < 6}
4792((OPTION_D)) {x: -3 ≤ x ≤ 6}
4793((CORRECT_CHOICE)) (A/B/C/D) C
4794((EXPLANATION)) (OPTIONAL) For numbers greater than -3, {x > -3} or {-3 < x} For numbers less than 6, {x < 6} Combine these to get, {x: -3 < x < 6}
4795
4796((MARKS)) (1/2/3...) 1
4797((QUESTION)) The number of elements in the Power set P(S) of the set S =
4798 [ [ Φ] , 1, [ 2, 3 ]] is
4799((OPTION_A)) 2
4800((OPTION_B)) 4
4801((OPTION_C)) 8
4802((OPTION_D)) None
4803((CORRECT_CHOICE)) (A/B/C/D) C
4804((EXPLANATION)) (OPTIONAL)
4805
4806
4807((MARKS)) (1/2/3...) 1
4808((QUESTION)) If A and B are sets and A∪ B= A ∩ B, then
4809((OPTION_A)) A = Φ
4810((OPTION_B)) B = Φ
4811((OPTION_C)) A = B
4812((OPTION_D)) none of these
4813((CORRECT_CHOICE)) (A/B/C/D) C
4814((EXPLANATION)) (OPTIONAL)
4815
4816((MARKS)) (1/2/3...) 1
4817((QUESTION)) Let S be an infinite set and S1, S2, S3, ..., Sn be sets such
4818 that S1 ∪S2∪S3∪ .......Sn = S then
4819((OPTION_A)) atleast one of the sets Si is a finite set
4820((OPTION_B)) not more than one of the set Si can be inite
4821((OPTION_C)) atleast one of the sets Si is an ininite set
4822((OPTION_D)) none of these
4823((CORRECT_CHOICE)) (A/B/C/D) C
4824((EXPLANATION)) (OPTIONAL)
4825
4826
4827((MARKS)) (1/2/3...) 1
4828((QUESTION)) In a room containing 28 people, there are 18 people who
4829speak English, 15 people who speak Hindi and 22 people
4830 who speak Kannada, 9 persons speak both English and
4831 Hindi, 11 persons speak both Hindi and Kannada where as
4832 13 persosn speak both Kannada and English. How many
4833 people speak all the three languages ?
4834((OPTION_A)) 6
4835((OPTION_B)) 7
4836((OPTION_C)) 8
4837((OPTION_D)) 9
4838((CORRECT_CHOICE)) (A/B/C/D) A
4839((EXPLANATION)) (OPTIONAL)
4840
4841((MARKS)) (1/2/3...) 1
4842((QUESTION)) Order of the power set of a set of order n is
4843((OPTION_A)) n
4844((OPTION_B)) 2n
4845((OPTION_C)) n^2
4846((OPTION_D)) 2^n
4847((CORRECT_CHOICE)) (A/B/C/D) D
4848((EXPLANATION)) (OPTIONAL)
4849
4850
4851((MARKS)) (1/2/3...) 1
4852((QUESTION)) In a beauty contest, half the number of experts voted for
4853 Mr. A and two thirds voted for Mr. B. 10 voted for both and
4854 6 did not vote for either. How many experts were there in all ?
4855((OPTION_A)) 18
4856((OPTION_B)) 36
4857((OPTION_C)) 24
4858((OPTION_D)) None
4859((CORRECT_CHOICE)) (A/B/C/D) C
4860((EXPLANATION)) (OPTIONAL)
4861
4862((MARKS)) (1/2/3...) 1
4863((QUESTION)) Which of the following statements is FALSE
4864((OPTION_A)) 2 ∈ A ∪ B implies that if 2 ∈/ A then 2 ∈ B.
4865((OPTION_B)) {2, 3} ⊆ A implies that 2 ∈ A and 3 ∈ A.
4866((OPTION_C)) A ∩ B ⊇ {2, 3} implies that {2, 3} ⊆ A and {2, 3} ⊆ B.
4867((OPTION_D)) {2} ∈ A and {3} ∈ A implies that {2, 3} ⊆ A.
4868((CORRECT_CHOICE)) (A/B/C/D) D
4869((EXPLANATION)) (OPTIONAL)
4870
4871
4872((MARKS)) (1/2/3...) 1
4873((QUESTION)) Which of the following statements is TRUE?
4874((OPTION_A)) For all sets A, B, and C, A − (B − C) = (A − B) – C
4875((OPTION_B)) For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) – B
4876((OPTION_C)) For all sets A, B, and C, (A − B) ∩ (C − B) = A − (B ∪ C).
4877((OPTION_D)) For all sets A, B, and C, if A ∩ C = B ∩ C then A = B
4878((CORRECT_CHOICE)) (A/B/C/D) B
4879((EXPLANATION)) (OPTIONAL)
4880
4881((MARKS)) (1/2/3...) 1
4882((QUESTION)) Which of the following statements is FALSE?
4883((OPTION_A)) C − (B ∪ A) = (C − B) – A
4884((OPTION_B)) A − (C ∪ B) = (A − B) – C
4885((OPTION_C)) B − (A ∪ C) = (B − C) – A
4886((OPTION_D)) A − (B ∪ C) = (B − C) − A
4887((CORRECT_CHOICE)) (A/B/C/D) D
4888((EXPLANATION)) (OPTIONAL)
4889
4890((MARKS)) (1/2/3...) 1
4891((QUESTION)) Consider the true theorem, “For all sets A and B, if A ⊆ B then A ∩ Bc = ∅.”
4892 Which of the following statements is NOT equivalent to this statement:
4893((OPTION_A)) For all sets Ac and B, if A ⊆ B then Ac ∩ Bc = ∅.
4894((OPTION_B)) For all sets A and B, if Ac ⊆ B then Ac ∩ Bc = ∅.
4895((OPTION_C)) For all sets Ac and Bc , if A ⊆ Bc then A ∩ B = ∅
4896((OPTION_D)) For all sets Ac and Bc , if Ac ⊆ Bc then Ac ∩ B = ∅
4897((CORRECT_CHOICE)) (A/B/C/D) A
4898((EXPLANATION)) (OPTIONAL)
4899
4900((MARKS)) (1/2/3...) 1
4901((QUESTION)) The power set P((A × B) ∪ (B × A)) has the same number of elements as the
4902 power set P((A × B) ∪ (A × B)) if and only if
4903((OPTION_A)) A = B
4904((OPTION_B)) A = ∅ or B = ∅
4905((OPTION_C)) B = ∅ or A = B
4906((OPTION_D)) A = ∅ or B = ∅ or A = B
4907((CORRECT_CHOICE)) (A/B/C/D) D
4908((EXPLANATION)) (OPTIONAL)
4909
4910((MARKS)) (1/2/3...) 1
4911((QUESTION)) A={a, b} and B={1, 2, 3}, what is the value of (A cross B) intersection ( B cross A)
4912
4913((OPTION_A)) { a}
4914
4915((OPTION_B)) { b}
4916
4917((OPTION_C)) {1, 2, 3}
4918
4919((OPTION_D)) null set
4920
4921((CORRECT_CHOICE)) (A/B/C/D) D
4922((EXPLANATION)) (OPTIONAL)
4923
4924((MARKS)) (1/2/3...) 1
4925((QUESTION)) Warshall algorithm can be used to find –
4926
4927((OPTION_A)) Composition
4928((OPTION_B)) Transitive relation
4929((OPTION_C)) Negation
4930((OPTION_D)) poset
4931((CORRECT_CHOICE)) (A/B/C/D) B
4932((EXPLANATI
4933
4934
4935((MARKS)) (1/2/3...) 1
4936((QUESTION)) Equivalence relation must not satisfy --
4937
4938((OPTION_A)) Antisymmetric
4939((OPTION_B)) Reflexive
4940((OPTION_C)) Symmetric
4941((OPTION_D)) Transitive
4942((CORRECT_CHOICE)) (A/B/C/D) A
4943((EXPLANATION)) (OPTIONAL)
4944
4945((MARKS)) (1/2/3...) 1
4946((QUESTION)) partial order relation is reflexive , transitive and ?
4947
4948((OPTION_A)) antisymmetric
4949
4950((OPTION_B)) symmeric
4951
4952((OPTION_C)) asymmetric
4953
4954((OPTION_D)) none
4955
4956((CORRECT_CHOICE)) (A/B/C/D) A
4957((EXPLANATION)) (OPTIONAL)
4958
4959
4960((MARKS)) (1/2/3...) 1
4961((QUESTION)) A crossproduct B = B crossproduct A , where A , B is matrix then
4962
4963((OPTION_A)) A is empty
4964
4965((OPTION_B)) B is empty
4966
4967((OPTION_C)) A equal to B
4968
4969((OPTION_D)) none
4970
4971((CORRECT_CHOICE)) (A/B/C/D) C
4972((EXPLANATION)) (OPTIONAL)
4973
4974((MARKS)) (1/2/3...) 1
4975((QUESTION)) If A= { 1,2,{1,2}} then P(P(A)) has
4976
4977((OPTION_A)) 4 elements
4978
4979((OPTION_B)) 8 elements
4980
4981((OPTION_C)) 256 elements
4982
4983((OPTION_D)) 16 elements
4984
4985((CORRECT_CHOICE)) (A/B/C/D) C
4986((EXPLANATION)) (OPTIONAL)
4987
4988
4989((MARKS)) (1/2/3...) 1
4990((QUESTION)) if A is set of children in family then relation - " x is brother of y " on set A is ?
4991
4992((OPTION_A)) reflexive
4993
4994((OPTION_B)) symmetric,transitive
4995
4996((OPTION_C)) antisymmetric
4997
4998((OPTION_D)) none
4999
5000((CORRECT_CHOICE)) (A/B/C/D) B
5001((EXPLANATION)) (OPTIONAL)
5002
5003((MARKS)) (1/2/3...) 1
5004((QUESTION)) The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
5005
5006((OPTION_A)) Reflexive
5007
5008((OPTION_B)) Transitive
5009
5010((OPTION_C)) Symmetric
5011
5012((OPTION_D)) Asymmetric
5013
5014((CORRECT_CHOICE)) (A/B/C/D) B
5015((EXPLANATION)) (OPTIONAL)
5016
5017
5018((MARKS)) (1/2/3...) 1
5019
5020((QUESTION)) Find the number of relations from A = {cat, dog, rat} to B = {male , female}
5021
5022((OPTION_A)) 64
5023((OPTION_B)) 6
5024((OPTION_C)) 56
5025((OPTION_D)) 128
5026((CORRECT_CHOICE)) (A/B/C/D) A
5027((EXPLANATION)) (OPTIONAL)
5028
5029((MARKS)) (1/2/3...) 1
5030((QUESTION)) For f: A ->B , the co-domain set is ,
5031
5032((OPTION_A)) A
5033((OPTION_B)) B
5034((OPTION_C)) Both A,B
5035((OPTION_D)) none
5036((CORRECT_CHOICE)) (A/B/C/D) B
5037((EXPLANATION)) (OPTIONAL)
5038
5039
5040((MARKS)) (1/2/3...) 1
5041((QUESTION)) Which is recurrence relation for fibonacci series ---
5042
5043((OPTION_A)) fn = f(n-2) + f(n-1)
5044((OPTION_B)) fn = f(n-2) - f(n-1)
5045((OPTION_C)) fn = f(n-2) * f(n-1)
5046((OPTION_D)) None
5047((CORRECT_CHOICE)) (A/B/C/D) A
5048((EXPLANATION)) (OPTIONAL)
5049
5050((MARKS)) (1/2/3...) 1
5051((QUESTION)) If A,B are disjoint sets and (A,B) belongs to relation R then
5052
5053((OPTION_A)) R is symmetric
5054
5055((OPTION_B)) R is reflexive
5056
5057((OPTION_C)) R is transitive
5058
5059((OPTION_D)) antisymmetric
5060
5061((CORRECT_CHOICE)) (A/B/C/D) A
5062((EXPLANATION)) (OPTIONAL)
5063
5064
5065((MARKS)) (1/2/3...) 1
5066((QUESTION)) If A= { 0,{1,2}, {} } then P(A) has
5067((OPTION_A)) 4 elements
5068((OPTION_B)) 8 elements
5069((OPTION_C)) 256 elements
5070((OPTION_D)) 16 elements
5071((CORRECT_CHOICE)) (A/B/C/D) B
5072((EXPLANATION)) (OPTIONAL)
5073
5074((MARKS)) (1/2/3...) 1
5075((QUESTION)) If A= { a,b,{a,c},{} } then {a,c} - A = ?
5076((OPTION_A)) {a,b}
5077((OPTION_B)) {b , {a,c}}
5078((OPTION_C)) { c }
5079((OPTION_D)) None
5080((CORRECT_CHOICE)) (A/B/C/D) C
5081((EXPLANATION)) (OPTIONAL)
5082
5083
5084((MARKS)) (1/2/3...) 1
5085((QUESTION)) if f and g are 2 functions then fog is called as –
5086
5087((OPTION_A)) Inverse
5088((OPTION_B)) Composite
5089((OPTION_C)) recurence
5090((OPTION_D)) None
5091((CORRECT_CHOICE)) (A/B/C/D) B
5092((EXPLANATION)) (OPTIONAL)
5093
5094((MARKS)) (1/2/3...) 1
5095((QUESTION)) function can’t be
5096
5097((OPTION_A)) One-one
5098((OPTION_B)) Onto
5099((OPTION_C)) One to many
5100((OPTION_D)) Many to one
5101((CORRECT_CHOICE)) (A/B/C/D) C
5102((EXPLANATION)) (OPTIONAL)
5103
5104
5105((MARKS)) (1/2/3...) 2
5106((QUESTION)) If A={2,3,5,6,10,15,30} and aRb if a|b then (A,R) is
5107((OPTION_A)) Lattice
5108((OPTION_B)) Poset
5109((OPTION_C)) poset having LUB
5110((OPTION_D)) None
5111((CORRECT_CHOICE)) (A/B/C/D) C
5112((EXPLANATION)) (OPTIONAL)
5113
5114
5115((MARKS)) (1/2/3...) 2
5116((QUESTION)) The number of distinct relations on a set of 3 elements is
5117((OPTION_A)) 8
5118((OPTION_B)) 9
5119((OPTION_C)) 18
5120((OPTION_D)) 512
5121((CORRECT_CHOICE)) (A/B/C/D) D
5122((EXPLANATION)) (OPTIONAL)
5123
5124
5125((MARKS)) (1/2/3...) 2
5126((QUESTION)) Hasse diagram is used to ,represent ?
5127((OPTION_A)) Poset
5128((OPTION_B)) Subset
5129((OPTION_C)) null set
5130((OPTION_D)) None
5131((CORRECT_CHOICE)) (A/B/C/D) A
5132((EXPLANATION)) (OPTIONAL)
5133
5134
5135
5136
5137
5138((MARKS)) (1/2/3...) 2
5139((QUESTION)) S={1,2,3….,8,9} find which is valid partition ?
5140((OPTION_A)) Null set
5141((OPTION_B)) {{S}}
5142((OPTION_C)) { null set}
5143((OPTION_D)) None
5144((CORRECT_CHOICE)) (A/B/C/D) B
5145((EXPLANATION)) (OPTIONAL)
5146
5147
5148((MARKS)) (1/2/3...) 2
5149((QUESTION)) X = {1,2,3,4,5} , A = {{1,2},{3,4,5}} , B = { {1,2,3} ,{4}}
5150((OPTION_A)) both A , B are valid partition
5151((OPTION_B)) both A , B are invalid partition
5152((OPTION_C)) A is valid but B is invalid
5153((OPTION_D)) None
5154((CORRECT_CHOICE)) (A/B/C/D) C
5155((EXPLANATION)) (OPTIONAL)
5156
5157((MARKS)) (1/2/3...) 2
5158((QUESTION)) S = {(a,b)| a,b are real nos. And 1+ab > 0 } then relation S -
5159((OPTION_A)) Reflexive,symmetric
5160((OPTION_B)) symmetric,transitive
5161((OPTION_C)) Equivalence
5162((OPTION_D)) only transitive
5163((CORRECT_CHOICE)) (A/B/C/D) A
5164((EXPLANATION)) (OPTIONAL)
5165
5166
5167((MARKS)) (1/2/3...) 2
5168((QUESTION)) R is relation defined on Z as ab> = 0 then R is
5169((OPTION_A)) Equivalence
5170((OPTION_B)) symmetric,transitive
5171((OPTION_C)) Reflexive
5172((OPTION_D)) None
5173((CORRECT_CHOICE)) (A/B/C/D) A
5174((EXPLANATION)) (OPTIONAL)
5175
5176((MARKS)) (1/2/3...) 2
5177((QUESTION)) Cross product of 2 sets is ,
5178
5179((OPTION_A)) Commutative
5180((OPTION_B)) Associative
5181((OPTION_C)) Distributive
5182((OPTION_D)) None
5183((CORRECT_CHOICE)) (A/B/C/D) D
5184((EXPLANATION)) (OPTIONAL)
5185
5186
5187((MARKS)) (1/2/3...) 2
5188((QUESTION)) if either set A is empty OR set B is empty, then cross product is,
5189
5190((OPTION_A)) Empty
5191((OPTION_B)) Disjoint
5192((OPTION_C)) Equal
5193((OPTION_D)) None
5194((CORRECT_CHOICE)) (A/B/C/D) A
5195((EXPLANATION)) (OPTIONAL)
5196
5197((MARKS)) (1/2/3...) 1
5198((QUESTION)) Transitive closure is obtained using
5199
5200((OPTION_A)) Tree
5201((OPTION_B)) Graph
5202((OPTION_C)) Stack
5203((OPTION_D)) Queue
5204((CORRECT_CHOICE)) (A/B/C/D) B
5205((EXPLANATION)) (OPTIONAL)
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233UNIT 3
5234
5235(Q)1 :Let * be a binary operation on a set A. The operation * is said to be
5236associative if
5237(A) (a * b) * c = a * (b * c)
5238(B) (a * b * c) = (a * b) * c
5239(C) (a * c) * b = a * (b * c)
5240(D) None of these
5241(E) A
5242.
5243(Q)1 :If (A, *) be an algebraic system where * is a binary operation on A. If ∀ x ∈ A,
5244e * x = x then e is called.
5245(A) Left identity
5246(B) Right identity
5247(C) Identity
5248(D) Inverse
5249(E) A
5250.
5251(Q)1 :If (A, *) be an algebraic system where * is a binary operation on A. If ∀ x ∈ A, x
5252* e = x then e is called
5253(A) Left identity
5254(B) Right identity
5255(C) Identity
5256(D) Inverse
5257(E) B
5258.
5259(Q)1 :If e 1 is left identity and e 2 is right identity of an algebraic system (A, *) then
5260(A) e 1 ≠ e 2
5261(B) e 1 < e 2
5262(C) e 1 > e 2
5263(D) e 1 = e 2
5264(E) D
5265.
5266(Q)1 :Let A be the set of all positive even integers {2, 4, 6, …}. Identity which
5267operations is closed on set A.
5268(A) Addition
5269(B) Subtraction
5270(C) Division
5271(D) None of these
5272(E) A
5273.
5274(Q)1 :Let (A, *) be an algebraic system where * is a binary operation on A. Then (A,*) is called
5275semigroup if
5276(A) * is closed
5277(B) * is association
5278(C) * is commutative
5279(D) both a and b
5280(E) D
5281.
5282(Q)1 :If (A, *) be an Algebraic system, where * is a binary operation on A. (A, *) is
5283called monoid if
5284(A) * is closed
5285(B) * is associative
5286(C) There is an identity
5287(D) All three
5288(E) D
5289.
5290(Q)2 :Let (A, *) be an algebraic system with an identity e. :Let a be an element in A,
5291and b * a = e then b is said to be
5292(A) Left inverse of a
5293(B) Right inverse of a
5294(C) Inverse of a
5295(D) None of these
5296(E) A
5297.
5298(Q)2 :Let (A, *) be an algebraic system with an identity element e. :Let a be an
5299element in A and a * b = e then b is said to be
5300(A) Left inverse of a
5301(B) Right inverse of a
5302(C) Inverse of a
5303(D) None of there
5304(E) B
5305.
5306(Q)2 :Let (A, *) be an algebraic system, where * is a binary operation, (A, *) is called
5307group if
5308(A) * is closed and associative
5309(B) There is an identity
5310(C) Every element in A has left inverse
5311(D) All three
5312(E) D
5313.
5314(Q)1 :Let (A, +) is a monoid when identity element is 0. If B ⊆ A and B is the closed
5315under the operation + and identity element 0 ∈ B, then (B, +) is called.
5316(A) Monoid
5317(B) submonoid
5318(C) semigroup
5319(D) group
5320(E) B
5321.
5322(Q)2 :Let (A, *) be an algebraic system, then which is the right identity.
5323* α β γ δ
5324α α β δ γ
5325β β α γ δ
5326γ γ δ α β
5327δ δ δ β γ
5328(A) α
5329(B) β
5330(C) γ
5331(D) δ
5332(E) A
5333.
5334(Q)2 :Let (A, *) be an algebraic system, then which is the left identity.
5335* α β γ δ
5336α δ α β γ
5337β α β γ δ
5338γ α β γ γ
5339δ α β γ δ
5340(A) α and β
5341(B) β and γ
5342(C) β and δ
5343(D) δ and γ
5344(E) C
5345.
5346(Q)1 : The set of all real numbers under the usual multiplication operation is not a
5347group since
5348(A) multiplication is not a binary operation
5349(B) multiplication is not associative
5350(C) Identity element does not exist
5351(D) Zero has no inverses
5352(E) D
5353.
5354(Q)2 :If (G, .) is a group such that (ab) –1 = a –1 b –1 , ∀ a, b ∈ G, then G is a / an
5355(A) Commutative semi group
5356(B) Ablian group
5357(C) Non ablian group
5358(D) None of these
5359(E) C
5360.
5361(Q)1 :If (G, .) is a group such that a 2 = e, ∀ a ∈ G then G is
5362(A) Semigroup
5363(B) Ablian group
5364(C) Non-ablian group
5365(D) None of these
5366(E) B
5367.
5368(Q)2 : The Inverse of – i in the multiplicative group (1, – 1,i, –i) is
5369(A) 1
5370(B) – 1
5371(C) i
5372(D) – i
5373(E) C
5374.
5375(Q)4 : The set of integers Z with the binary operation * defined as a * b = a + b + 1
5376for a, b ∈ z, is a group. The identity element of this group is
5377(A) 0
5378(B) 1
5379(C) –1
5380(D) 12
5381(E) C
5382.
5383(Q)4 : The group (G, *) , the value of (a –1 b) –1 is
5384(A) ab –1
5385(B) b –1 a
5386(C) a –1 b
5387(D) ba –1
5388(E) B
5389.
5390(Q)2 :If (G, .) is a group such that (ab) 2 = a 2 b 2 ∀ a, b ∈ Z then G is an
5391(A) Commutative semi group
5392(B) Abilian group
5393(C) Non-abilia group
5394(D) None of these
5395(E) B
5396.
5397(Q)4 : (Z, .) is a group, with a*b = a + b + 1 ∀ a b ∈ G, inverse of a is
5398(A) 0
5399(B) – 2
5400(C) a – 2
5401(D) – a – 2
5402(E) D
5403.
5404(Q)2 :Let G denoted the set of all n × n non-singular matrices with rational numbers
5405as entries. Then under multiplication G is a/an
5406(A) Sub group
5407(B) Finite ablian group
5408(C) Infinite non-ablian of group
5409(D) Infinite ablian
5410(E) C
5411.
5412(Q)2 :Let A be the set of all non singular matrices our dual numbers and Let * be the
5413matrix multiplication operator then
5414(A) A is closed * but < A, * > is not a semigroup
5415(B) <A, * > is a semigroup but not a monoid
5416(C) <A, * > is a monoid but not a group
5417(D) <A, *> is a group but not an ablian group
5418(E) D
5419.
5420(Q)2 :If a, b are positive integers define a * b = a where ab = a (module 7) with this
5421* operation then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is
5422(A) 3
5423(B) 1
5424(C) 5
5425(D) 4
5426(E) C
5427.
5428(Q)2 : Which of the following is true
5429(A) Set of all rational negative number form a group under multiplication
5430(B) Set of all non singular matrix form a group under multiplication
5431(C) Set of all matrices forms a group under multiplication
5432(D) Both
5433(B) and
5434(C)
5435(E) B
5436.
5437(Q)2 : The set of all n th roots of unity under multiplication of complex numbers from a/
5438An
5439(A) Semigroup with identify
5440(B) Commutative semigroups with identify
5441(C) Group
5442(D) Abilian group
5443(E) D
5444.
5445(Q)2 : Which of the following is false
5446(A) The set of rational numbers is an abilian group under addition
5447(B) The set of rational integers is an abilian group under addition
5448(C) The set of rational number forms an abilian group under multiplication
5449(D) None of these
5450(E) C
5451.
5452(Q)1 : In the group G = {2, 4, 6, 8} under multiplication module 10. The identify
5453element is
5454(A) 6
5455(B) 8
5456(C) 4
5457(D) 2
5458(E) A
5459.
5460(Q)4 : Match the following
5461(A) Groups I. Associative
5462(B) Semigroups II. Identify
5463(C) Monoids III. Commutation
5464(D) Abilian group IV. Left inverse
5465Codes A, B, C, D
5466(A) IV, I, II, III
5467(B) III, I, IV, II
5468(C) II, III, I, IV
5469(D) I, II, III, IV
5470(E) A
5471.
5472(Q)4 :Let (z, *) be an algebraic structure where z is the set of integers and the
5473operation * is defined by n * m = amx (n, m) which of the following statements
5474is true for (z, *).
5475(A) (z, *) is a monoid
5476(B) (z, *) is an abilian group
5477(C) (z, *) is a group
5478(D) None of above
5479(E) D
5480.
5481(Q)2 : Consider the set Σ * of all string over the alphabet Σ = {0, 1}. Σ * with the
5482concatenation operator for string
5483(A) Does not form a group
5484(B) Does not have a right identify element
5485(C) Form a non commutative group
5486(D) None of these
5487(E) A
5488.
5489(Q)2 : The set {1, 2, 3, 5, 7, 8, 9} under the multiplication module 10 is not a group.
5490Given below are the four reasons. Which of them are false
5491(A) It is not closed
5492(B) 2 does not have an inverse
5493(C) 3 does not have an inverse
5494(D) 8 does not have an inverse
5495(E) C
5496.
5497(Q)4 : Let N be a set of positive integers, then which operation is not closed on the
5498set N.
5499(A) +, –
5500(B) *, –
5501(C) /, –
5502(D) +, *
5503(E) C
5504.
5505Explanation :
5506Because the difference (–) and division (/) of positive integers need not to be
5507positive integers
5508e.g. (2 – 9) = – 7 (not positive)
5509(7/3) = 2.3 (not positive integers)
5510(Q)2 :Let S = {0, 1, – 1}. Then addition which one is not an operation on S.
5511(A) +
5512(B) +,*
5513(C) *
5514(D) none of these
5515(E) A
5516.
5517(Q)2 :Let A and B denote respectively, the set of even and odd positive integers.
5518Then which statement is true.
5519(A) A is closed under addition and multiplication and B is under multiplied
5520(B) A is closed under addition and B is closed under addition multiplication
5521(C) A is closed under multiplication and B is closed under addition
5522(D) A is closed under multiplication and B is closed under addition and
5523multiplication
5524(E) A
5525.
5526(Q)1 :Let S = then which one is operation on S
5527(A) +, *
5528(B) –, +
5529(C) *, –
5530(D) /, +
5531(E) A
5532.
5533(Q)1 :Let S = then which is true ?
5534(A) S is closed under matrix addition
5535(B) S is closed under matrix multiplication
5536(C) S is closed under both
5537(D) S is closed under subtraction
5538(E) A
5539.
5540(Q)2 : An operation * on a set S is said to satisfy the left cancelation low if
5541(A) a * b = a * c ⇒ b = c
5542(B) a * c = b * a ⇒ b = a
5543(C) a * b = b * c ⇒ b = c
5544(D) None of these
5545(E) A
5546.
5547(Q)2 : An operation * on a set S is said to satisfy the right cancellation low if
5548(A) b * a = c * a ⇒ b = c
5549(B) c * a = a * b ⇒ a = c
5550(C) a * b = c * b ⇒ a = c
5551(D) None of these
5552(E) A
5553.
5554(Q)1 :Let S be a nonempty set with an operation and if the operation is associative
5555has an identify element then S is called
5556(A) Group
5557(B) Semigroup
5558(C) Monoid
5559(D) None of these
5560(E) C
5561.
5562(Q)1 : If G is a nonempty set with a binary operation and if the operation holds
5563associative identify and inverse then G is called
5564(A) Monoid
5565(B) Semigroup
5566(C) Group
5567(D) Abilian
5568(E) C
5569.
5570(Q)1 : If group G holds the commutative law then it is called
5571(A) Monoid
5572(B) Semigroup
5573(C) Group
5574(D) Abilian
5575(E) D
5576.
5577(Q)4 : Let (z, *) be an algebraic structure, where z is the set of integers and the
5578operation * is defined by n * m = max (n, m) which of the following statement
5579is true for (z, *) ?
5580(A) (z, *) is amonid
5581(B) (z, *) is an abelian group
5582(C) (z, *) is a group
5583(D) none of these
5584(E) B
5585.
5586(Q)4 : Some group (G, 0) is known to be abilian. Then which one of the following is
5587true for G. ?
5588(A) g = g – 1 for every g ∈ G
5589(B) g = g 2 for every g ∈ G
5590(C) (goh) 2 = g 2 oh 2 for every g, h, ∈ G
5591(D) G is finite order
5592(E) C
5593.
5594(Q)4 : If the binary operation * is defined on a set of order pairs of real number as (a,
5595b) * (c, d) = (ad + bc, bd) and is associative then
5596(1, 2) * (3, 5) * (3, 4) equals
5597(A) (74, 40)
5598(B) (32, 40)
5599(C) (23, 11)
5600(D) (7, 11)
5601(E) A
5602.
5603(Q)2 : A subset H of a group (G, *) is a group if
5604(A) a, b, ∈ H ⇒ a *b ∈ H
5605(B) a ∈ H ⇒ a –1 ∈ H
5606(C) a, b ∈ H ⇒ a *b –1 ∈ H
5607(D) H contains the identify element
5608(E) C
5609.
5610(Q)2 : G {e, a, b, c} is an abilian group with ‘e’ as identify element. The order of the
5611other elements are
5612(A) 2, 2, 3
5613(B) 3, 3, 3
5614(C) 2, 2, 4
5615(D) 2, 3, 4
5616(E) A
5617.
5618(Q)1 :If every element of a group G is its own inverse then G is
5619(A) Finite
5620(B) Infinite
5621(C) Cyclic
5622(D) Abilian 133
5623(E) D
5624.
5625(Q)1 : If A {0, 1}, A is closed under
5626(A) addition
5627(B) multiplication
5628(C) both addition and multiplication
5629(D) none of these
5630(E) B
5631.
5632(Q)2 : A non empty set G with binary operation ‘ ∗ ’ is a groupoid if
5633(A) ∀ a, b ∈ G ⇒ a ∗ b ∈ G
5634(B) ∀ a, b ∈ G ⇒ a ∗ b = b ∗ a
5635(C) both (A) and (B)
5636(D) None of these
5637(E)A
5638.
5639(Q)2 : Subtraction ‘–’ a binary rogation an
5640(A) set of natural numbers N
5641(B) set of whole numbers W
5642(C) set of integers I
5643(D) None of these
5644(E) C
5645.
5646(Q)2 : Division ‘ ÷ ’ is a binary operation as
5647(A) set of natural number N.
5648(B) set of whole number W
5649(C) set of integrals I
5650(D) set of rational number (Q)
5651(E) D
5652.
5653(Q)2 : Which is not an algebraic structure ?
5654(A) (N, –), N is set of natural numbers.
5655(B) (I, –), I is the set of integers
5656(C) (Q, –), Q is set of rational number
5657(D) (W, –), W is set of whole numbers
5658(E)A
5659.
5660(Q)2 : Which statement is false ?
5661(A) (I, +) satisfy the associative property.
5662(B) (I, .), satisfy the associative property.
5663(C) (I, –), satisfy associative property.
5664(D) None of these.
5665(E) C
5666.
5667(Q)4 : If N is the set of natural numbers and ∗ is a binary on N defined by
5668a ∗ b = a b , then 5 ∗ 2 is
5669(A) 10
5670(B) 7
5671(C) 25
5672(D) 32
5673(E) C
5674.
5675(Q)2 :If N is the set of national numbers and ∗ is a binary operation on N defined by
5676a ∗ b = a b , then
5677(A) ‘ ∗ ’ is commutative and associative on N.
5678(B) ‘ ∗ ’ is commutative but not associative on N.
5679(C) ‘ ∗ ’ is neither commutative or associative on N.
5680(D) ‘ ∗ ’ is associative but not commutative.
5681(E) C
5682.
5683(Q)2 :If A = {x/x is odd integers } and operation is multiplication ( ∗ ), then which is true
5684(A) A is closed under ‘ ∗ ’.
5685(B) A is associative under ‘ ∗ ’.
5686(C) both (A) and (B)
5687(D) None of these
5688(E) C
5689.
5690(Q)1 :If I is the set of integers and ‘ ∗ ’ multiplication is a binary operation defined an I
5691then (I, ∗ ) is
5692(A) group
5693(B) abelian group
5694(C) monoid
5695(D) none of these
5696(E) C
5697.
5698(Q)2 :If N is the set of natural numbers and multiplication ‘ ∗ ’ is a binary operation
5699then (N, ∗ ) is
5700(A) abelian group
5701(B) group but not abelian group
5702(C) monoid with commutative property
5703(D) monoid without commutative property
5704(E) C
5705.
5706(Q)2 :If A = {a/a is prime numbers} and operation is multiplication i.e. ‘ ∗ ’ then which
5707statement.
5708(A) A is closed under ‘ ∗ ’
5709(B) A is not closed under ‘ ∗ ’
5710(C) A is associative under ‘ ∗ ’
5711(D) both (B) and (C)
5712(E) D
5713.
5714(Q)4 : A non empty set G with binary operation ‘ ∗ ’ is an abelian group or
5715commutative group if.
5716(A) (G, ∗ ) is a groupoid and ∀ a, b ∈ G, a ∗ b = b ∗ a
5717(B) (G, ∗ ) is a semigroup and ∀ a, b ∈ G, a ∗ b = b ∗ a
5718(C) (G, ∗ ) is a monoid and ∀ a, b ∈ G, a ∗ b = b ∗ a
5719(D) (G, ∗ ) is a and ∀ a, b ∈ G, a ∗ b = b ∗ a
5720(E) D
5721.
5722(Q)2 :If I is set of integers and multiplication ‘ ∗ ’ is a binary operation defined on I
5723then (I, ∗ ) is
5724(A) group
5725(B) abelian group
5726(C) monoid
5727(D) none of these
5728(E) C
5729.
5730(Q)2 :If N is set of natural numbers and multiplication ‘ ∗ ’ is a binary operation then
5731(N, ∗ ) is
5732(A) abelian group
5733(B) group but not abelian group
5734(C) Monoid with commutative property
5735(D) monoid without commutative property
5736(E) C
5737.
5738(Q)2 :If W is the set of whole numbers and addition ‘+’ a binary operation defined on
5739W, then (W, +) is
5740(A) Abelian group
5741(B) group
5742(C) Monoid with commutative property
5743(D) Monoid with commutative property
5744(E) C
5745.
5746(Q)1 :If Q is set of rational numbers and multiplication is binary operation on Q, then
5747(Q, ∗ ) is
5748(A) group
5749(B) monoid
5750(C) abelian group
5751(D) none of these
5752(E) D
5753.
5754(Q)2 :If N is set of natural numbers and addition is a binary operation then which
5755statement is false ?
5756(A) (N, +) is monoid
5757(B) (N, +) is a group
5758(C) (N, +) is a semigroup
5759(D) (N, +) is a groupoid
5760(E) B
5761.
5762(Q)2 :If A is set of all sum integers with zero and ‘+’ is binary operation on A, then.
5763(A) (A, +) is a semigroup but not monoid
5764(B) (A, +) is a group but not abelian group
5765(C) (A, +) is a monoid but not group
5766(D) (A, +) is an abelian group
5767(E) C
5768.
5769(Q)2 :If A is set of all sum integers with zero and ‘.’ is binary operation on A, then.
5770(A) (A, .) is a semigroup but not monoid
5771(B) (A, .) is a group but not abelian group
5772(C) (A, .) is a monoid but not group
5773(D) (A, .) is an abelian group
5774(E) A
5775.
5776(Q)2 :If A is set of all odd integers with operation addition ‘+’ on A then.
5777(A) (A, +) is not an algebraic structure
5778(B) (A, +) is an algebraic structure
5779(C) (A, +) is simigroup
5780(D) (A, +) is monoid
5781(E) A
5782.
5783(Q)2 :If A is set of all odd integers with binary operation multiplication ‘ ∗ ’ on A, then.
5784(A) (A, ∗ ) is not an algebraic structure
5785(B) (A, ∗ ) is monoid
5786(C) (A, ∗ ) is a group
5787(D) (A, ∗ ) is abelian group
5788(E) B
5789.
5790(Q)4 :If G = {Even, odd} and binary operation ‘ ∗ ’ is defined as
5791∗ Even Odd
5792Even Even Odd
5793Odd Odd Even
5794Then (G, ∗ ) is
5795(A) semigroup but not monoid
5796(B) monoid but not group
5797(C) group but not abelian group
5798(D) abelian group
5799(E) D
5800.
5801(Q)4 :If S = […, – 2m, – m, 0, m, 2m, 3m] when m is a fixed integer then which
5802statement is true.
5803(A) (S, ∗ ) is an abelian group
5804(B) (So, ∗ ) is an abelian group
5805(C) (S, +) is an abelian group
5806(D) None of these
5807(E) C
5808.
5809(Q)2 :If Q is set of rational number then which statement is false :
5810(A) (Q, +) is an abelian group
5811(B) (Q, ∗ ) is an abelian group
5812(C) (Q 0 , ∗ ) is an abelian group
5813(D) None of these
5814(E) B
5815.
5816(Q)2 :For ring Z 10 ={0,1,2,…g} of integer modulo 10,units of Z 10 are
5817(A) 0,1,3 & 7
5818(B) 0,1,7 & g
5819(C) 1,2,3 & 7
5820(D) 3,7 & g
5821(E) B
5822.
5823(Q)2 :For which of the following sets is a *a binary operation:
5824(A) Z + where a*b=a-b
5825(B) on R where a*b=min(a,b)
5826(C) on Z,where a*b=a b
5827(D) on Z + where a*b=a|b
5828(E) B
5829.
5830(Q)2 :For which of the following sets is * an associative binary operation :
5831(A) N,where a*b=min(a,b+2)
5832(B) R+,where a*b=a|b
5833(C) N,where a*b=max(a,b)
5834(D) on R,where a*b=a|b
5835(E) C
5836.
5837(Q)2 :For which of the following sets is * an commutative binary operation :
5838(A) R,where a*b=a|b
5839(B) on R,where a*b=min(a,b)
5840(C) on R,where a*b= a b
5841(D) on N,where a*b=min(a,b+2)
5842(E) B
5843.
5844(Q)4 :Consider the binary operation table defined on the set A={a,b,c,d}
5845* A B C D
5846A b c a d
5847B c b a d
5848C a b c d
5849D d a b c
5850Then a*(b*c) is equal to
5851(A) a
5852(B) b
5853(C) c
5854(D) d
5855(E) B
5856.
5857(Q)4 :Consider the binary operation table defined on the set A={a,b,c,d}
5858* A B C D
5859A a c b d
5860B d a b c
5861C c d a a
5862D d b a c
5863Then (a*b)*d is equal to
5864(A) a
5865(B) b
5866(C) c
5867(D) d
5868(E) A
5869.
5870(Q)2 :The inverse and order of the element [3] in (Z 12 ,*) is :
5871(A) [6],2
5872(B) [9],3
5873(C) 6[3],3
5874(D) [3],3
5875(E) B
5876.
5877(Q)2 :The solution of the equation [7]+x=[5] in (Z 6 ,+) is :
5878(A) x=[4]
5879(B) x=[2]
5880(C) x=[3]
5881(D) x=[1]
5882(E) A
5883
58841. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
5885 A.
58861
58872
5888 B.
58892
58905
5891
5892C.
58938
589415
5895 D.
58969
589720
5898
5899Answer & Explanation
5900Answer: Option D
5901Explanation:
5902Here, S = {1, 2, 3, 4, ...., 19, 20}.
5903Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
5904 P(E) = n(E) = 9 .
5905 n(S) 20
5906
5907________________________________________
59082. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
5909 A.
591010
591121
5912 B.
591311
591421
5915
5916C.
59172
59187
5919 D.
59205
59217
5922
5923Answer & Explanation
5924Answer: Option A
5925Explanation:
5926Total number of balls = (2 + 3 + 2) = 7.
5927Let S be the sample space.
5928Then, n(S) = Number of ways of drawing 2 balls out of 7
5929 = 7C2 `
5930 = (7 x 6)
5931 (2 x 1)
5932
5933 = 21.
5934Let E = Event of drawing 2 balls, none of which is blue.
5935 n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.
5936 = 5C2
5937 = (5 x 4)
5938 (2 x 1)
5939
5940 = 10.
5941 P(E) = n(E) = 10 .
5942 n(S) 21
5943
5944________________________________________
59453. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
5946 A.
59471
59483
5949 B.
59503
59514
5952
5953C.
59547
595519
5956 D.
59578
595821
5959
5960E.
59619
596221
5963
5964Answer & Explanation
5965Answer: Option A
5966Explanation:
5967Total number of balls = (8 + 7 + 6) = 21.
5968Let E = event that the ball drawn is neither red nor green
5969 = event that the ball drawn is blue.
5970 n(E) = 7.
5971 P(E) = n(E) = 7 = 1 .
5972 n(S) 21 3
5973
5974________________________________________
59754. What is the probability of getting a sum 9 from two throws of a dice?
5976 A.
59771
59786
5979 B.
59801
59818
5982
5983C.
59841
59859
5986 D.
59871
598812
5989
5990Answer & Explanation
5991Answer: Option C
5992Explanation:
5993In two throws of a dice, n(S) = (6 x 6) = 36.
5994Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
5995 P(E) = n(E) = 4 = 1 .
5996 n(S) 36 9
5997
5998________________________________________
59995. Three unbiased coins are tossed. What is the probability of getting at most two heads?
6000 A.
60013
60024
6003 B.
60041
60054
6006
6007C.
60083
60098
6010 D.
60117
60128
6013
6014Answer & Explanation
6015Answer: Option D
6016Explanation:
6017Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
6018Let E = event of getting at most two heads.
6019Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
6020 P(E) = n(E) = 7 .
6021 n(S) 8
6022
6023
6024
60256. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
6026 A.
60271
60282
6029 B.
60303
60314
6032
6033C.
60343
60358
6036 D.
60375
603816
6039
6040Answer & Explanation
6041Answer: Option B
6042Explanation:
6043In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
6044Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
6045 (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
6046 (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
6047 n(E) = 27.
6048 P(E) =
6049n(E) = 27 = 3 .
6050 n(S) 36 4
6051View Answer Workspace Report Discuss in Forum
6052
6053________________________________________
60547. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
6055 A.
605621
605746
6058 B.
605925
6060117
6061
6062C.
60631
606450
6065 D.
60663
606725
6068
6069Answer & Explanation
6070Answer: Option A
6071Explanation:
6072Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
6073Then, n(S) = Number ways of selecting 3 students out of 25
6074 = 25C3 `
6075 = (25 x 24 x 23)
6076 (3 x 2 x 1)
6077
6078 = 2300.
6079n(E) = (10C1 x 15C2)
6080 =
608110 x (15 x 14)
6082
6083 (2 x 1)
6084
6085 = 1050.
6086 P(E) =
6087n(E) = 1050 = 21 .
6088 n(S) 2300 46
6089
6090________________________________________
60918. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
6092 A.
60931
609410
6095 B.
60962
60975
6098
6099C.
61002
61017
6102 D.
61035
61047
6105
6106Answer & Explanation
6107Answer: Option C
6108Explanation:
6109P (getting a prize) = 10 = 10 = 2 .
6110 (10 + 25) 35 7
6111
6112________________________________________
61139. From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
6114 A.
61151
611615
6117 B.
611825
611957
6120
6121C.
612235
6123256
6124 D.
61251
6126221
6127
6128Answer & Explanation
6129Answer: Option D
6130Explanation:
6131Let S be the sample space.
6132Then, n(S) = 52C2 = (52 x 51) = 1326.
6133 (2 x 1)
6134Let E = event of getting 2 kings out of 4.
6135 n(E) = 4C2 =
6136(4 x 3) = 6.
6137 (2 x 1)
6138 P(E) =
6139n(E) = 6 = 1 .
6140 n(S) 1326 221
6141
6142________________________________________
614310. Two dice are tossed. The probability that the total score is a prime number is:
6144 A.
61451
61466
6147 B.
61485
614912
6150
6151C.
61521
61532
6154 D.
61557
61569
6157
6158Answer & Explanation
6159Answer: Option B
6160Explanation:
6161Clearly, n(S) = (6 x 6) = 36.
6162Let E = Event that the sum is a prime number.
6163Then E = { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
6164 (5, 2), (5, 6), (6, 1), (6, 5) }
6165 n(E) = 15.
6166 P(E) =
6167n(E) = 15 = 5 .
6168 n(S) 36 12
6169
6170
6171
6172
617311. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
6174 A.
61751
617613
6177 B.
61782
617913
6180
6181C.
61821
618326
6184 D.
61851
618652
6187
6188Answer & Explanation
6189Answer: Option C
6190Explanation:
6191Here, n(S) = 52.
6192Let E = event of getting a queen of club or a king of heart.
6193Then, n(E) = 2.
6194 P(E) =
6195n(E) = 2 = 1 .
6196 n(S) 52 26
6197
6198________________________________________
619912. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
6200 A.
62011
620222
6203 B.
62043
620522
6206
6207C.
62082
620991
6210 D.
62112
621277
6213
6214Answer & Explanation
6215Answer: Option C
6216Explanation:
6217Let S be the sample space.
6218Then, n(S) = number of ways of drawing 3 balls out of 15
6219 = 15C3
6220 = (15 x 14 x 13)
6221 (3 x 2 x 1)
6222
6223 = 455.
6224Let E = event of getting all the 3 red balls.
6225 n(E) = 5C3 = 5C2 =
6226(5 x 4) = 10.
6227 (2 x 1)
6228 P(E) =
6229n(E) = 10 = 2 .
6230 n(S) 455 91
6231
6232________________________________________
623313. Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
6234 A.
62353
623620
6237 B.
623829
623934
6240
6241C.
624247
6243100
6244 D.
624513
6246102
6247
6248Answer & Explanation
6249Answer: Option D
6250Explanation:
6251Let S be the sample space.
6252Then, n(S) = 52C2 = (52 x 51) = 1326.
6253 (2 x 1)
6254Let E = event of getting 1 spade and 1 heart.
6255 n(E)
6256= number of ways of choosing 1 spade out of 13 and 1 heart out of 13
6257 = (13C1 x 13C1)
6258 = (13 x 13)
6259 = 169.
6260 P(E) =
6261n(E) = 169 = 13 .
6262 n(S) 1326 102
6263
6264________________________________________
626514. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
6266 A.
62671
626813
6269 B.
62703
627113
6272
6273C.
62741
62754
6276 D.
62779
627852
6279
6280Answer & Explanation
6281Answer: Option B
6282Explanation:
6283Clearly, there are 52 cards, out of which there are 12 face cards.
6284 P (getting a face card) = 12 = 3 .
6285 52 13
6286
6287________________________________________
628815. A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
6289 A.
62903
62914
6292 B.
62934
62947
6295
6296C.
62971
62988
6299 D.
63003
63017
6302
6303Answer & Explanation
6304Answer: Option B
6305Explanation:
6306Let number of balls = (6 + 8) = 14.
6307Number of white balls = 8.
6308P (drawing a white ball) = 8 = 4 .
6309 14 7
6310
6311 16. In a throw of coin what is the probability of getting head.
63121. 1
63132. 2
63143. 1/2
63154. 0
6316Answer And Explanation
6317Answer: Option C
6318Explanation:
6319Total cases = [H,T] - 2
6320Favourable cases = [H] -1
6321So probability of getting head = 1/2
632217. In a throw of coin what is the probability of getting tails.
63231. 1
63242. 2
63253. 1/2
63264. 0
6327Answer And Explanation
6328Answer: Option C
6329Explanation:
6330Total cases = [H,T] - 2
6331Favourable cases = [T] -1
6332So probability of getting tails = 1/2
6333
633418. Two unbiased coins are tossed. What is probability of getting at most one tail ?
63351. 12
63362. 13
63373.32
63384.34
63394. •
6340Answer And Explanation
6341Answer: Option D
6342Explanation:
6343Total 4 cases = [HH, TT, TH, HT]
6344Favourable cases = [HH, TH, HT]
6345Please note we need atmost one tail, not atleast one tail.
6346
6347So probability = 3/4
6348
634919. Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?
63501. 1/3
63512. 1/6
63523. 1/2
63534. 1/8
6354Answer And Explanation
6355Answer: Option C
6356Explanation:
6357Total cases are = 2*2*2 = 8, which are as follows
6358[TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]
6359
6360Favoured cases are = [TTH, THT, HTT, TTT] = 4
6361
6362So required probability = 4/8 = 1/2
6363
636420. In a throw of dice what is the probability of getting number greater than 5
63651. 1/2
63662. 1/3
63673. 1/5
63684. 1/6
6369Answer And Explanation
6370Answer: Option D
6371Explanation:
6372Number greater than 5 is 6, so only 1 number
6373Total cases of dice = [1,2,3,4,5,6]
6374
6375So probability = 1/6
6376
637721. What is the probability of getting a sum 9 from two throws of dice.
63781. 1/3
63792. 1/9
63803. 1/12
63814. 2/9
6382Answer And Explanation
6383Answer: Option B
6384Explanation:
6385Total number of cases = 6*6 = 36
6386
6387Favoured cases = [(3,6), (4,5), (6,3), (5,4)] = 4
6388
6389So probability = 4/36 = 1/9
6390
639122. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?
63921. 3/4
63932. 1/4
63943. 7/4
63954. 1/2
6396Answer And Explanation
6397Answer: Option A
6398Explanation:
6399Total number of cases = 6*6 = 36
6400
6401Favourable cases = [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),
6402(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27
6403
6404So Probability = 27/36 = 3/4
6405
640623. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
64071. 2/3
64082. 8/21
64093. 3/7
64104. 9/22
6411Answer And Explanation
6412Answer: Option B
6413Explanation:
6414Total number of balls = (8 + 7 + 6) = 21
6415Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
6416Therefore, n(E) = 8.
6417P(E) = 8/21.
6418
6419
642024. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
64211. 1/13
64222. 2/13
64233. 1/26
64244. 1/52
6425Answer And Explanation
6426Answer: Option C
6427Explanation:
6428Total number of cases = 52
6429Favourable cases = 2
6430
6431Probability = 2/56 = 1/26
6432
643325. From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.
64341. 4/13
64352. 1/52
64363. 1/4
64374. None of above
6438Answer And Explanation
6439Answer: Option A
6440Explanation:
6441Total number of cases = 52
6442Total face cards = 16 [favourable cases]
6443
6444So probability = 16/52 = 4/13
6445
6446
6447
644826. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
64491. 719
64502. 619
6451 3. 519
6452 4. 419
64534. •
645427. A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident
64551. 30%
64562. 35%
64573. 40%
64584. 45%
6459Answer And Explanation
6460Answer: Option B
6461Explanation:
6462Let A = Event that A speaks the truth
6463B = Event that B speaks the truth
6464
6465Then P(A) = 75/100 = 3/4
6466P(B) = 80/100 = 4/5
6467
6468P(A-lie) = 1-3/4 = 1/4
6469P(B-lie) = 1-4/5 = 1/5
6470
6471Now
6472A and B contradict each other =
6473[A lies and B true] or [B true and B lies]
6474= P(A).P(B-lie) + P(A-lie).P(B)
6475[Please note that we are adding at the place of OR]
6476= (3/5*1/5) + (1/4*4/5) = 7/20
6477= (7/20 * 100) % = 35%
6478
6479
648028. From a pack of 52 cards, two cards are drawn together, what is the probability that both the cards are kings
64811. 2/121
64822. 2/221
64833. 1/221
64844. 1/13
6485Answer And Explanation
6486Answer: Option C
6487Explanation:
6488Total cases =52C2=52∗512∗1=1326Total King cases =4C2=4∗32∗1=6Probability ==61326=1221
648929. A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour.
64901. 52/55
64912. 3/55
64923. 41/44
64934. 3/44
6494Answer And Explanation
6495Answer: Option C
6496Explanation:
6497Total cases =12C3=12∗11∗103∗2∗1=220Total cases of drawing same colour =5C3+4C3+3C35∗42∗1+4+1=15Probability of same colur ==15220=344Probability of not same colur =1−344=4144
6498
649930. Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that ball is white
65001. 1
65012. 2/3
65023. 1/3
65034. 4/3
6504Answer And Explanation
6505Answer: Option B
6506Explanation:
6507Total cases = 10 + 20 = 30
6508Favourable cases = 20
6509
6510So probability = 20/30 = 2/3
6511
651231. There is a pack of 52 cards and Rohan draws two cards together, what is the probability that one is spade and one is heart ?
65131. 11/102
65142. 13/102
65153. 11/104
65164. 11/102
6517Answer And Explanation
6518Answer: Option B
6519Explanation:
6520Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
6521
6522Let sample space be S
6523
6524then, n(S) = 52C2=>52×512×1=1326let E be event of getting 1 spade and 1 heart So, n(E) = ways of getting 1 spade or 1 heart out of 13=13C1×13C1=13×13=169So, p(E) = n(E)n(S)=1691326=13102
6525
652632. If I calculate the probability of an event and it turns out to be -.7, I know that
6527 A. the event is probably going to happen.
6528 B. the event is probably not going to happen.
6529 C. the probability of it not happening is .3.
6530 D. I made a mistake.
6531
6532________________________________________
6533
653433. If I flip a fair coin 10 times, which of the following is true?
6535 A. The number of heads will equal the number of tails.
6536 B. The probability of all heads is greater than the probability of all tails.
6537 C. The probability of HHHHHHHHHH = the probability of HTHTHTHTHT.
6538 D. The probability of HHHHHHHHHH < the probability of HTHTHTHTHT.
6539
6540________________________________________
6541
654234. Which of the following facts does a person ignore when they reason with the gambler's fallacy?
6543 A. Probabilities describe outcomes over the very long term.
6544 B. Extreme outcomes are always counteracted by equally extreme opposite outcomes.
6545 C. The likelihood of the winning depends on the other players.
6546 D. Only fair dice are used at gambling casinos.
6547
6548________________________________________
6549
655035. Which of the following are likely to be dependent events?
6551 A. the weather and the number of books on your shelf
6552 B. the color of your car and its gas mileage
6553 C. the weight of your car and its gas mileage
6554 D. the size of your house and the size of your shoes
6555
6556________________________________________
6557
655836. If I sample with replacement, which of the following may be true?
6559 A. The numerator for the next event's probability changes.
6560 B. The denominator for the next event's probability changed.
6561 C. Both the numerator and denominator for the next event's probability change.
6562 D. None of the values used in calculating the next event's probability change.
6563
6564________________________________________
6565
6566
6567
6568
656937. If I am selecting subjects to be in my study, I necessarily must do sampling without replacement (I can not have the same person in my study twice). What effect does this have on the sample selection process?
6570 A. All subject selection is random.
6571 B. Subjects can no longer be chosen randomly.
6572 C. Each time I select a subject, the people remaining in the subject pool have less of a chance of getting picked.
6573 D. Each time I select a subject, the people remaining in the subject pool have more of a chance of getting picked.
6574
6575________________________________________
6576
657738. I know that if I draw a single card from a deck, it can not be a red card and a black card because these are
6578 A. colors.
6579 B. not in the deck.
6580 C. mutually exclusive.
6581 D. conditional.
6582
6583________________________________________
6584
658539. In studying the services available to homeless people at different shelters, I find that only .05 take advantage of job training. This seems small. I decide to investigate further and I see that of the people who were offered job training .65 accepted it. The value .65 is a
6586 A. percentage.
6587 B. small number.
6588 C. conditional probability.
6589 D. mutual exclusion.
6590
6591________________________________________
6592
659340. The weight of US Postal Service packages is normally distributed with a mean of 2 oz. and a standard deviation of .5 oz. If I choose two letters from my mail carrier's bag, what is the probability that they will both weigh less than 1 oz.?
6594 A. .0005
6595 B. .0228
6596 C. .0456
6597 D. .4772
6598
6599________________________________________
6600
660141. What does a p-value tell you?
6602 A. the likelihood of the results obtained in a study deviating from a conservative expectation of no difference
6603 B. if you have conducted your study correctly
6604 C. if you can use the binomial distribution to calculate your probabilities
6605 D. the likelihood that you are correct
6606
6607________________________________________
6608
660942. Multiple- Question Scenarios I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course.
6610Using the given data, answer the following question.
6611COURSE
6612 Pass Fail
6613FINAL
6614Pass 142 34
6615Fail 89 56
6616What is the probability that a student, taken at random from my class, would have passed my course?
6617 A. .72
6618 B. .61
6619 C. .44
6620 D. .55
6621
6622________________________________________
6623
6624
6625
662643. Multiple- Question Scenarios I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course.
6627Using the given data, answer the following question.
6628COURSE
6629 Pass Fail
6630FINAL
6631Pass 142 34
6632Fail 89 56
6633What is the probability that a student, taken at random from my class, would have passed the final?
6634 A. .72
6635 B. .61
6636 C. .44
6637 D. .55
6638
6639________________________________________
6640
664144. Multiple- Question Scenarios I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course.
6642Using the given data, answer the following question.
6643COURSE
6644 Pass Fail
6645FINAL
6646Pass 142 34
6647Fail 89 56
6648What is the probability that a student, taken at random from my class, would have passed the class and the final?
6649 A. .72
6650 B. .61
6651 C. .44
6652 D. .55
6653
6654________________________________________
6655
665645. Multiple- Question Scenarios I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course.
6657Using the given data, answer the following question.
6658COURSE
6659 Pass Fail
6660FINAL
6661Pass 142 34
6662Fail 89 56
6663What is the probability that a student, taken at random from my class, would have passed the class, given that they failed the final?
6664 A. .72
6665 B. .61
6666 C. .44
6667 D. .55
6668
6669________________________________________
6670
667146. I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course.
6672Using the given data, answer the following question.
6673COURSE
6674 Pass Fail
6675FINAL
6676Pass 142 34
6677Fail 89 56
6678What is the probability that a student, taken at random from my class, would have failed the class, given that they failed the final?
6679 A. .72
6680 B. .61
6681 C. .44
6682 D. .39
6683
668447.The probability of getting a head in tossing of a coin is
6685
66860.5
6687
66881
6689
66901.5
6691
6692-0.5
6693
669448.. The probability of an event cannot be
6695
66961
6697
66980.3
6699
67000.5
6701
6702-0.5
6703
670449. A bag contains 10 red balls and 7 blue balls. A ball is drawn at random. The probability that ball drawn is not red is
6705
67067
6707
67087/17
6709
671010/17
6711
67123/17
6713
671450. A bag contains 12 red balls and 10 blue balls. A ball is drawn at random. The probability that ball drawn is red is
6715
671612
6717
67186/11
6719
67205/11
6721
67221
6723
672451. A bag contains 7 white balls and 10 black balls. A ball is drawn at random. The probability that ball drawn is black is
6725
672610/17
6727
672810
6729
67307/17
6731
67321
6733
6734MCQ QUESTIONS ON PERMUTATION AND COMBINATION
6735
67361. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
6737 A.
6738564 B.
6739645
6740C.
6741735 D.
6742756
6743E.
6744None of these
6745
67462.
6747Answer: Option D
6748Explanation:
6749We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
6750 Required number of ways = (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
6751 = 7 x 6 x 5 x 6 x 5 + (7C3 x 6C1) + (7C2)
6752 3 x 2 x 1 2 x 1
6753
6754 = 525 + 7 x 6 x 5 x 6 + 7 x 6
6755 3 x 2 x 1 2 x 1
6756
6757 = (525 + 210 + 21)
6758 = 756.
6759
67602. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
6761 A.
6762360 B.
6763480
6764C.
6765720 D.
67665040
6767E.
6768None of these
6769
67703.
6771Answer: Option C
6772Explanation:
6773The word 'LEADING' has 7 different letters.
6774When the vowels EAI are always together, they can be supposed to form one letter.
6775Then, we have to arrange the letters LNDG (EAI).
6776Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
6777The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
6778 Required number of ways = (120 x 6) = 720.
67793. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
6780 A.
6781810 B.
67821440
6783C.
67842880 D.
678550400
6786E.
67875760
6788
6789
6790Answer: Option D
6791Explanation:
6792In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
6793Thus, we have CRPRTN (OOAIO).
6794This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
6795Number of ways arranging these letters = 7! = 2520.
6796 2!
6797Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
6798in 5! = 20 ways.
6799 3!
6800
68014. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
6802 A.
6803210 B.
68041050
6805C.
680625200 D.
680721400
6808E.
6809None of these
6810
6811
6812
68135. In how many ways can the letters of the word 'LEADER' be arranged?
6814 A.
681572 B.
6816144
6817C.
6818360 D.
6819720
6820E.
6821None of these
6822
6823Answer: Option C
6824Explanation:
6825The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
6826 Required number of ways = 6! = 360.
6827 (1!)(2!)(1!)(1!)(1!)
6828
68296. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
6830 A.
6831159 B.
6832194
6833C.
6834205 D.
6835209
6836E.
6837None of these
6838
6839Answer: Option D
6840Explanation:
6841We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
6842 Required number
6843of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
6844 = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
6845 = (6 x 4) + 6 x 5 X 4 x 3 + 6 x 5 x 4 x 4 + 6 x 5
6846 2 x 1 2 x 1 3 x 2 x 1 2 x 1
6847
6848 = (24 + 90 + 80 + 15)
6849 = 209.
68507. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
6851 A.
68525 B.
685310
6854C.
685515 D.
685620
6857
6858Answer: Option D
6859Explanation:
6860Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
6861The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
6862The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
6863 Required number of numbers = (1 x 5 x 4) = 20.
6864
68658. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
6866 A.
6867266 B.
68685040
6869C.
687011760 D.
687186400
6872E.
6873None of these
6874
6875Answer: Option C
6876Explanation:
6877Required number of ways = (8C5 x 10C6)
6878 = (8C3 x 10C4)
6879 = 8 x 7 x 6 x 10 x 9 x 8 x 7
6880 3 x 2 x 1 4 x 3 x 2 x 1
6881
6882 = 11760.
68839. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
6884 A.
688532 B.
688648
6887C.
688864 D.
688996
6890E.
6891None of these
6892
6893Answer: Option C
6894Explanation:
6895We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
6896 Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
6897 = 3 x 6 x 5 + 3 x 2 x 6 + 1
6898 2 x 1 2 x 1
6899
6900 = (45 + 18 + 1)
6901 = 64.
690210. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
6903 A.
690432 B.
690548
6906C.
690736 D.
690860
6909E.
6910120
6911
6912Answer: Option C
6913Explanation:
6914There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
6915Let us mark these positions as under:
6916(1) (2) (3) (4) (5) (6)
6917Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
6918Number of ways of arranging the vowels = 3P3 = 3! = 6.
6919Also, the 3 consonants can be arranged at the remaining 3 positions.
6920Number of ways of these arrangements = 3P3 = 3! = 6.
6921Total number of ways = (6 x 6) = 36.
692211. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
6923 A.
692463 B.
692590
6926C.
6927126 D.
692845
6929E.
6930135
6931
6932Answer: Option A
6933Explanation:
6934Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = 7 x 6 x 3 = 63.
6935 2 x 1
6936
693712. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
6938 A.
693940 B.
6940400
6941C.
69425040 D.
69432520
6944
6945Answer: Option C
6946Explanation:
6947'LOGARITHMS' contains 10 different letters.
6948Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
6949 = 10P4
6950 = (10 x 9 x 8 x 7)
6951 = 5040.
695213. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
6953 A.
695410080 B.
69554989600
6956C.
6957120960 D.
6958None of these
6959
6960
6961Answer: Option C
6962Explanation:
6963In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
6964Thus, we have MTHMTCS (AEAI).
6965Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
6966 Number of ways of arranging these letters = 8! = 10080.
6967 (2!)(2!)
6968Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
6969Number of ways of arranging these letters = 4! = 12.
6970 2!
6971 Required number of words = (10080 x 12) = 120960.
6972
697314. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
6974 A.
6975120 B.
6976720
6977C.
69784320 D.
69792160
6980E.
6981None of these
6982
6983
6984Answer: Option B
6985Explanation:
6986The word 'OPTICAL' contains 7 different letters.
6987When the vowels OIA are always together, they can be supposed to form one letter.
6988Then, we have to arrange the letters PTCL (OIA).
6989Now, 5 letters can be arranged in 5! = 120 ways.
6990The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
6991 Required number of ways = (120 x 6) = 720.
699215. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
6993A. 24400 B. 21300
6994C. 210 D. 25200
6995
6996Answer: Option D
6997Explanation:
6998Number of ways of selecting 3 consonants from 7
6999= 7C3
7000Number of ways of selecting 2 vowels from 4
7001= 4C2
7002
7003Number of ways of selecting 3 consonants from 7 and 2 vowels from 4
7004= 7C3 × 4C2
7005=(7×6×53×2×1)×(4×32×1)=210=(7×6×53×2×1)×(4×32×1)=210
7006
7007It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
7008
7009Number of ways of arranging 5 letters among themselves
7010=5!=5×4×3×2×1=120=5!=5×4×3×2×1=120
7011
7012Hence, required number of ways
7013=210×120=25200
701416. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
7015A. 159 B. 209
7016C. 201 D. 212
7017Answer: Option B
7018Explanation:
7019In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
7020
7021Hence we have 4 options as given below
7022
7023We can select 4 boys ...(option 1)
7024Number of ways to this = 6C4
7025
7026We can select 3 boys and 1 girl ...(option 2)
7027Number of ways to this = 6C3 × 4C1
7028
7029We can select 2 boys and 2 girls ...(option 3)
7030Number of ways to this = 6C2 × 4C2
7031
7032We can select 1 boy and 3 girls ...(option 4)
7033Number of ways to this = 6C1 × 4C3
7034
7035Total number of ways
7036= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
7037= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
7038=6×52×1+6×5×43×2×1×4=6×52×1+6×5×43×2×1×4 +6×52×1×4×32×1+6×4+6×52×1×4×32×1+6×4
7039=15+80+90+24=209
7040
704117. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
7042A. 624 B. 702
7043C. 756 D. 812
7044Answer: Option C
7045Explanation:
7046From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
7047
7048Hence we have the following 3 options.
7049
7050We can select 5 men ...(option 1)
7051Number of ways to do this = 7C5
7052
7053We can select 4 men and 1 woman ...(option 2)
7054Number of ways to do this = 7C4 × 6C1
7055
7056We can select 3 men and 2 women ...(option 3)
7057Number of ways to do this = 7C3 × 6C2
7058
7059Total number of ways
7060= 7C5 + (7C4 × 6C1) + (7C3 × 6C2)
7061= 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]
7062=7×62×1+7×6×53×2×1×6=7×62×1+7×6×53×2×1×6 +7×6×53×2×1×6×52×1+7×6×53×2×1×6×52×1
7063=21+210+525=756
7064
706518. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
7066A. 610 B. 720
7067C. 825 D. 920
7068
7069Answer: Option B
7070Explanation:
7071The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).
7072
7073Hence we can assume total letters as 5 and all these letters are different.
7074Number of ways to arrange these letters
7075=5!=5×4×3×2×1=120=5!=5×4×3×2×1=120
7076
7077All the 3 vowels (OIA) are different
7078Number of ways to arrange these vowels among themselves
7079=3!=3×2×1=6=3!=3×2×1=6
7080
7081Hence, required number of ways
7082=120×6=720
708319. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
7084A. 47200 B. 48000
7085C. 42000 D. 50400
7086
7087Answer: Option D
7088Explanation:
7089The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).
7090
7091Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.
7092
7093Number of ways to arrange these letters
7094=7!2!=7×6×5×4×3×2×12×1=2520=7!2!=7×6×5×4×3×2×12×1=2520
7095
7096In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.
7097
7098Number of ways to arrange these vowels among themselves =5!3!=5×4×3×2×13×2×1=20=5!3!=5×4×3×2×13×2×1=20
7099
7100Hence, required number of ways
7101=2520×20=50400=2520×20=50400
710220. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
7103A. 1 B. 126
7104C. 63 D. 64
7105Answer: Option C
7106Explanation:
7107We need to select 5 men from 7 men and 2 women from 3 women.
7108
7109Number of ways to do this
7110= 7C5 × 3C2
7111= 7C2 × 3C1 [∵ nCr = nC(n-r)]
7112=7×62×1×3=21×3=63
7113
711421. In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
7115A. 9800 B. 100020
7116C. 120960 D. 140020
7117Answer: Option C
7118Explanation:
7119The word 'MATHEMATICS' has 11 letters. It has the vowels 'A','E','A','I' in it and these 4 vowels must always come together. Hence these 4 vowels can be grouped and considered as a single letter. That is, MTHMTCS(AEAI).
7120
7121Hence we can assume total letters as 8. But in these 8 letters, 'M' occurs 2 times, 'T' occurs 2 times but rest of the letters are different.
7122
7123Hence, number of ways to arrange these letters
7124=8!(2!)(2!)=8!(2!)(2!) =8×7×6×5×4×3×2×1(2×1)(2×1)=10080=8×7×6×5×4×3×2×1(2×1)(2×1)=10080
7125
7126In the 4 vowels (AEAI), 'A' occurs 2 times and rest of the vowels are different.
7127
7128Number of ways to arrange these vowels among themselves =4!2!=4×3×2×12×1=12=4!2!=4×3×2×12×1=12
7129
7130Hence, required number of ways
7131=10080×12=120960
7132
713322. There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?
7134A. 10420 B. 11
7135C. 11760 D. None of these
7136
7137Answer: Option C
7138Explanation:
7139We need to select 5 men from 8 men and 6 women from 10 women
7140
7141Number of ways to do this
7142= 8C5 × 10C6
7143= 8C3 × 10C4 [∵ nCr = nC(n-r)]
7144=(8×7×63×2×1)(10×9×8×74×3×2×1)=56×210=11760=(8×7×63×2×1)(10×9×8×74×3×2×1)=56×210=11760
714523. How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
7146A. 720 B. 420
7147C. None of these D. 5040
7148
7149Answer: Option A
7150Explanation:
7151The word 'LOGARITHMS' has 10 different letters.
7152
7153Hence, the number of 3-letter words(with or without meaning) formed by using these letters
7154= 10P3
7155=10×9×8=720=10×9×8=720
715610. In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
7157A. None of these B. 720
7158C. 420 D. 122
7159Answer: Option B
7160Explanation:
7161The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).
7162
7163Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters
7164=5!=5×4×3×2×1=120=5!=5×4×3×2×1=120
7165
7166In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves
7167=3!=3×2×1=6=3!=3×2×1=6
7168
7169Hence, required number of ways
7170=120×6=720
717124. A coin is tossed 3 times. Find out the number of possible outcomes.
7172A. None of these B. 8
7173C. 2 D. 1
7174Answer: Option B
7175Explanation:
7176When a coin is tossed once, there are two possible outcomes: Head(H) and Tale(T)
7177
7178Hence, when a coin is tossed 3 times, the number of possible outcomes
7179=2×2×2=8=2×2×2=8
7180
7181(The possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT )
7182
718325. In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?
7184A. None of these B. 64
7185C. 120 D. 36
7186
7187Answer: Option D
7188Explanation:
7189The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
7190
7191The 3 vowels(EAI) must occupy only the odd positions. Let's mark the positions as (1) (2) (3) (4) (5) (6). Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
7192
7193Hence, number of ways to arrange these vowels
7194= 3P3 =3!=3×2×1=6=3!=3×2×1=6
7195
7196Now we have 3 consonants(DTL) which can be arranged in the remaining 3 positions in any order. Hence, number of ways to arrange these consonants
7197= 3P3=3!=3×2×1=6=3!=3×2×1=6
7198
7199Total number of ways
7200= number of ways to arrange the vowels × number of ways to arrange the consonants
7201=6×6=36
720226. A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?
7203A. 64 B. 128
7204C. 32 D. None of these
7205
7206Answer: Option A
7207Explanation:
7208From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that at least one black ball should be there.
7209
7210Hence we have 3 choices as given below
7211
7212We can select 3 black balls...(option 1)
7213We can select 2 black balls and 1 non-black ball ...(option 2)
7214We can select 1 black ball and 2 non-black balls ...(option 3)
7215
7216Number of ways to select 3 black balls
7217= 3C3
7218Number of ways to select 2 black balls and 1 non-black ball
7219= 3C2 × 6C1
7220Number of ways to select 1 black ball and 2 non-black balls
7221= 3C1 × 6C2
7222
7223Total number of ways
7224= 3C3 + 3C2 × 6C1 + 3C1 × 6C2
7225= 3C3 + 3C1 × 6C1 + 3C1 × 6C2[∵ nCr = nC(n-r)]
7226=1+3×6+3×6×52×1=1+18+45=64=1+3×6+3×6×52×1=1+18+45=64
722727. In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?
7228A. None of these B. 48
7229C. 32 D. 64
7230
7231Answer: Option B
7232Explanation:
7233The word 'JUDGE' has 5 letters. It has 2 vowels (UE) and these 2 vowels should always come together. Hence these 2 vowels can be grouped and considered as a single letter. That is, JDG(UE).
7234
7235Hence we can assume total letters as 4 and all these letters are different. Number of ways to arrange these letters
7236=4!=4×3×2×1=24=4!=4×3×2×1=24
7237
7238In the 2 vowels (UE), all the vowels are different. Number of ways to arrange these vowels among themselves
7239=2!=2×1=2=2!=2×1=2
7240
7241Total number of ways =24×2=48
7242
724328. In how many ways can the letters of the word 'LEADER' be arranged?
7244A. None of these B. 120
7245C. 360 D. 720
7246
7247Answer: Option C
7248Explanation:
7249The word 'LEADER' has 6 letters.
7250
7251But in these 6 letters, 'E' occurs 2 times and rest of the letters are different.
7252
7253Hence,number of ways to arrange these letters
7254=6!2!=6×5×4×3×2×12×1=360
7255
725629. How many words can be formed by using all letters of the word 'BIHAR'?
7257A. 720 B. 24
7258C. 120 D. 60
7259
7260Answer: Option C
7261Explanation:
7262The word 'BIHAR' has 5 letters and all these 5 letters are different.
7263
7264Total number of words that can be formed by using all these 5 letters
7265= 5P5 =5!=5!
7266=5×4×3×2×1=120
726730. How many arrangements can be made out of the letters of the word 'ENGINEERING' ?
7268A. 924000 B. 277200
7269C. None of these D. 182000
7270Answer: Option B
7271Explanation:
7272The word 'ENGINEERING' has 11 letters.
7273
7274But in these 11 letters, 'E' occurs 3 times,'N' occurs 3 times, 'G' occurs 2 times, 'I' occurs 2 times and rest of the letters are different.
7275
7276Hence,number of ways to arrange these letters
7277=11!(3!)(3!)(2!)(2!)=11×10×9×8×7×6×5×4×3×2(3×2)(3×2)(2)(2)=277200
7278
727931. How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
7280A. 20 B. 16
7281C. 8 D. 24
7282
7283Answer: Option A
7284Explanation:
7285A number is divisible by 5 if the its last digit is 0 or 5
7286
7287
7288
7289We need to find out how many 3 digit numbers can be formed from the 6 digits (2,3,5,6,7,9)(2,3,5,6,7,9) which are divisible by 5.
7290
7291Since the 3 digit number should be divisible by 5, we should take the digit 5 from the 6 digits(2,3,5,6,7,9) and fix it at the unit place. There is only 1 way of doing this.
7292 1
7293Since the number 5 is placed at unit place, we have now five digits(2,3,6,7,9) remaining. Any of these 5 digits can be placed at tens place
7294 5 1
7295Since the digit 5 is placed at unit place and another one digit is placed at tens place, we have now four digits remaining. Any of these 4 digits can be placed at hundreds place.
72964 5 1
7297Required Number of three digit numbers
7298=4×5×1=20
7299
730032. How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?
7301A. 720 B. 24
7302C. None of these D. 120
7303
7304Answer: Option D
7305Explanation:
7306The word 'DELHI' has 5 letters and all these letters are different.
7307
7308Total number of words (with or without meaning) that can be formed using all these 5 letters using each letter exactly once
7309= Number of arrangements of 5 letters taken all at a time
7310= 5P5 =5!=5×4×3×2×1=120=5!=5×4×3×2×1=120
731133. What is the value of 100P2 ?
7312A. 9801 B. 12000
7313C. 5600 D. 9900
7314
7315Answer: Option D
7316Explanation:
7317100P2 =100×99=9900
731834. In how many different ways can the letters of the word 'RUMOUR' be arranged?
7319A. None of these B. 128
7320C. 360 D. 180
7321Answer: Option D
7322Explanation:
7323The word 'RUMOUR' has 6 letters.
7324
7325In these 6 letters, 'R' occurs 2 times, 'U' occurs 2 times and rest of the letters are different.
7326
7327Hence, number of ways to arrange these letters
7328=6!(2!)(2!)=6×5×4×3×22×2=180
7329
733035. There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
7331A. 3200 B. None of these
7332C. 1800 D. 3600
7333
7334Answer: Option C
7335Explanation:
7336Solution 1
7337
73385 subjects can be arranged in 6 periods in 6P5 ways.
7339
7340Any of the 5 subjects can be organized in the remaining period (5C1 ways).
7341
7342Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
7343
7344Total number of arrangements
7345= 6P5× 5C12!=1800
7346Solution 2
73475 subjects can be selected in 5C5 ways.
7348
73491 subject can be selected in 5C1 ways.
7350
7351These 6 subjects can be arranged themselves in 6! ways.
7352
7353Since two subjects are same, we need to divide by 2!
7354
7355Therefore, total number of arrangements
7356= 5C5× 5C1×6!2!=1800= 5C5× 5C1×6!2!=1800
7357________________________________________
7358Solution 3
7359Select any 5 periods (6C5 ways).
7360Allocate a different subject to each of these 5 periods (1 way).
7361These 5 subjects can be arranged themselves in 5! ways.
7362Select the 6th period (1 way).
7363Allocate a subject to this period (5C1 ways).
7364Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
7365Therefore, required number of ways
7366= 6C5×1×5!×1× 5C12!=1800= 6C5×1×5!×1× 5C12!=1800
7367________________________________________
7368
7369Solution 4
7370
7371
7372There are 5 subjects and 6 periods. Each subject must be allowed in at least one period. Therefore, two periods will have same subject and remaining four periods will have different subjects.
7373
7374Select the two periods where the same subject is taught. This can be done in 6C2 ways.
7375
7376Allocate a subject two these two periods(5C1 ways).
7377
7378Remaining 4 subjects can be arranged in the remaining 4 periods in 4! ways.
7379
7380Required number of ways
7381= 6C2 × 5C1 × 4! = 1800
738236. How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
7383A. 720 B. 360
7384C. 1420 D. 1680
7385Answer: Option D
7386Explanation:
7387The first two places can only be filled by 3 and 5 respectively and there is only 1 way for doing this.
7388
7389Given that no digit appears more than once. Hence we have 8 digits remaining (0,1,2,4,6,7,8,9)(0,1,2,4,6,7,8,9)
7390
7391So, the next 4 places can be filled with the remaining 8 digits in 8P4 ways.
7392
7393Total number of ways = 8P4 =8×7×6×5=1680
7394
739537. An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?
7396A. 100 B. 80
7397C. 110 D. 64
7398
7399Answer: Option B
7400Explanation:
7401He has 10 patterns of chairs and 8 patterns of tables
7402
7403A chair can be selected in 10 ways.
7404A table can be selected in 8 ways.
7405
7406Hence one chair and one table can be selected in 10×810×8 ways =80=80 ways
740738. 25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
7408A. None of these B. 600
7409C. 576 D. 625
7410Answer: Option B
7411Explanation:
7412He can go in any of the 25 buses (25 ways).
7413
7414Since he cannot come back in the same bus, he can return in 24 ways.
7415
7416Total number of ways =25×24=600
7417
741839. A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours?
7419A. 62 B. 48
7420C. 12 D. 24
7421
7422Answer: Option D
7423Explanation:
74241 red ball can be selected in 4C1 ways.
74251 white ball can be selected in 3C1 ways.
74261 blue ball can be selected in 2C1 ways.
7427
7428Total number of ways
7429= 4C1 × 3C1 × 2C1
7430=4×3×2=24
743140. A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?
7432A. None of these B. 6020
7433C. 1200 D. 9450
7434Answer: Option D
7435Explanation:
7436Number of ways to choose 8 questions from part P = 10C8
7437Number of ways to choose 4 questions from part Q = 10C4
7438
7439Total number of ways
7440= 10C8 × 10C4
7441= 10C2 × 10C4[∵ nCr = nC(n-r)]
7442=(10×92×1)(10×9×8×74×3×2×1)=45×210=9450
7443
744441. In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
7445A. 2880 B. 1400
7446C. 1200 D. 3212
7447
7448Answer: Option A
7449Explanation:
7450Around a circle, 5 boys can be arranged in 4! ways.
7451
7452Given that the boys and the girls alternate. Hence there are 5 places for the girls. Therefore the girls can be arranged in 5! ways.
7453
7454Total number of ways
7455=4!×5!=24×120=2880
745642. Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
7457A. 120 B. 720
7458C. 125 D. 729
7459
7460Answer: Option D
7461Explanation:
7462The first ring can be worn in any of the 3 fingers (3 ways).
7463
7464Similarly each of the remaining 5 rings also can be worn in 3 ways.
7465
7466Hence total number of ways
7467=3×3×3×3×3×3=36=729
746843. In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?
7469A. None of these B. 720
7470C. 60 D. 120
7471
7472Answer: Option D
7473Explanation:
74741st man can draw water from any of the 5 taps.
74752nd man can draw water from any of the remaining 4 taps.
74763rd man can draw water from any of the remaining 3 taps.
74774th man can draw water from any of the remaining 2 taps.
74785th man can draw water from remaining 1 tap.
74795 4 3 2 1
7480Hence total number of ways
7481=5×4×3×2×1=120
748244. In how many ways can 11 persons be arranged in a row such that 3 particular persons should always be together?
7483A. 9!×3!9!×3! B. 9!9!
7484C. 11!11! D. 11!×3!
7485
7486Answer: Option A
7487Explanation:
7488Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person.
7489
7490Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9!9! ways.
7491
7492We had grouped three persons together. These three persons can be arranged among themselves in 3!3! ways.
7493
7494Hence, required number of ways
7495=9!×3!=9!×3!
7496
749745. In how many ways can 9 different colour balls be arranged in a row so that black, white, red and green balls are never together?
7498A. 146200 B. 219600
7499C. 314562 D. 345600
7500Answer: Option D
7501Explanation:
7502Total number of ways in which 9 different colour balls can be arranged in a row
7503=9! ⋯=9! ⋯(A)
7504
7505Now we will find out total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are always together.
7506
7507We have total 9 balls. Since black, white, red and green balls are always together, group these 4 balls together and consider as a single ball. Hence we can take total number of balls as 6. These 6 balls can be arranged in 6!6! ways.
7508
7509We had grouped 4 balls together. These 4 balls can be arranged among themselves in 4!4!ways.
7510
7511Hence, total number of ways in which 9 different colour balls be arranged in a row so that black, white, red and green balls are always together
7512=6!×4! ⋯=6!×4! ⋯(B)
7513
7514From (A) and (B),
7515Total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together
7516=9!–6!×4!=6!×7×8×9−6!×4!=6!(7×8×9–4!)=6!(504–24)=6!×480=720×480=345600
7517
7518
7519
752046: Evaluate combination
7521100C97=100!(97)!(3)!100C97=100!(97)!(3)!
7522
7523A.161700
7524B.151700
7525C.141700
7526D.131700
7527
7528Answer: Option A
7529Explanation:
7530nCr=n!(r)!(n−r)!100C97=100!(97)!(3)!=100∗99∗98∗97!(97)!(3)!=100∗99∗983∗2∗1=100∗99∗983∗2∗1=161700
7531
753247. A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw
7533A.64
7534B.128
7535C:132
7536D:222
7537
7538Answer: Option A
7539Explanation:
7540From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that
7541at least one black ball should be there.
7542
7543Hence we have 3 choices
7544All three are black
7545Two are black and one is non black
7546One is black and two are non black
7547Total number of ways
7548= 3C3 + (3C2 x 6C1) + (3C1 x 6C2) [because 6 are non black]
7549=1+[3×6]+[3×(6×52×1)]=1+18+45=64
7550
7551
7552 OBJECTIVE QUESTION BANK : UNIT 1
7553Sr. No. Question Option 1 Option 2 Option 3 Option 4 Answer
75541 Way of getting information from measuring observation whose outcomes occurrence is on chance is called beta experiment random experiment alpha experiment gamma experiment Option 2
75552 Probability of second event in situation if first event has been occurred is classified as subjective approach objective approach intuitive approach sample approach Option 1
75563 In probability theories, events which can never occur together are classified as collectively exclusive events mutually exhaustive events mutually exclusive events collectively exhaustive events Option 3
75574 Joint probability of independent events J and K is equal to P(J) * P(K) P(J) + P(K) P(J) * P(K) + P(J-K) P(J) * P(K) - P(J * K) Option 1
75585 Consider two events X and Y, X-bar and Y-bar represents occurrence of Y occurrence of X non-occurrence of X and Y occurrence of X and Y Option 3
75596 In measuring probability of any certain event, zero represents impossible events possible events certain event sample event Option 1
75607 Variation in which outcomes of experiments are effected by uncontrolled factors is considered as random variation mesokurtic variation platykurtic variation mesokurtic variation Option 1
75618 If two events X and Y are considered as partially overlapping events then rule of addition can be written as P(X or Y) = P(X) - P(Y) + P(X and Y) P(X or Y) = P(X) + P(Y) * P(X - Y) P(X or Y) = P(X) * P(Y) + P(X - Y) P(X or Y) = P(X) + P(Y) - P(X and Y) Option 4
75629 If a person buys a lottery, chance of winning a Toyota car is 60%, chance of winning Hyundai car is 70% and chance of winning both is 40% then chance of winning Toyota or Hyundai is 0.6 0.9 0.8 0.5 Option 2
756310 According to combination rule, if total number of outcomes are 'r' and distinct outcome collection is 'n' then combinations are calculated as n! ⁄ r!(n - r)! n! ⁄ r!(n + r)! r! ⁄ n!(n - r)! r! ⁄ n!(n + r)! Option 1
756411 Outcomes of an experiment are classified as logged events exponential results results events Option 4
756512 For a random experiment, all possible outcomes are called numerical space event space sample space both b and c Option 4
756613 Types of probabilities for independent events must includes joint events marginal events conditional events all of above Option 4
756714 Probability with out any conditions of occurrence of an event is considered as conditional probability marginal probability non conditional probability occurrence probability Option 2
756815 In a Venn diagram used to represent probabilities, sample space of events is represented by square triangle circle rectangle Option 4
756916 Consider an event B, non occurrence of event B is represented by union of A complement of A intersection of A A is equal to zero Option 2
757017 If a brown sack consists of 4 white balls and 3 black balls then probability of one randomly drawn ball will be white is 4 ⁄ 7 1 ⁄7 4 ⁄ 4 4 ⁄ 3 Option 1
757118 Difference between sample space and subset of sample space is considered as numerical complementary events equal compulsory events complementary events compulsory events Option 3
757219 Occurrence of two events in a way that events have some connection in between is classified as compound events mutual events connected events interlinked events Option 1
757320 If a bag contains three fruits, 16 percent are apples, 30 percent are oranges and 20 percent some other fruit that is neither oranges nor apples then probability of selecting an orange randomly is 0.3 0.45 0.65 0.034 Option 1
757421 Method in which previously calculated probabilities are revised with new probabilities is classified as updating theorem revised theorem Bayes theorem dependency theorem Option 3
757522 Probability of events must lie in limits of one to two two to three one to two zero to one Option 4
757623 Event such as equal chance of heads or tails while tossing coin is an example of numerical events equally likely events unequal events non-numerical events Option 2
757724 If a coin is tossed one time then probability of occurrence of heads is 1⁄2 1⁄1 2⁄1 2⁄2 Option 1
757825 If a luggage bag contains two types of shirts, 40 percent are dress shirts, 45 percent are T-shirts and 30 percent are blue jeans then probability of selecting a dress shirt in random sample is 0.47 0.4 0.35 0.3 Option 2
757926 If in an experiment A and B are two events, then occurrence of event B or event A or occurrence of both is represented by A - B A union B A intersection B A + B Option 2
758027 Sample space for experiment in which two coins are tossed is 4 8 2 10 Option 1
758128 If factory has four machines, machines will be completely depreciated in next year and chances of failure of all machines respectively are 0.24, 0.45, 0.35, 0.38 then probability of failure of all machines before next year is 0.355 0.148 0.158 0.168 Option 4
758229 Consider the experiment of tossing a coin three timesw. What is the probability of getting one head? 3÷8 3÷8 3÷8 None of these Option 1
758330 A company selects marketing professionals on the basis of an aptitude test. Past experience indicates that only 75% of the candidates were found satisfactory, in actual marketing, 80% had passed the aptitude test. Only 20% of those found unsatisfactory, had passed the test. Given that a candidate passed the apptitude test, what is the probability that he would be found satisfactory. 0.923 0.9 22 None of these Option 1
758431 If A and B are two arbitrary events, then P(A∩B) cannot be less than P(A) +P(B)-1 Greater than P(A)+P(B) Equal to P(A)+P(B)-P(AUB) Equal to P(A)+P(B)+P(AUB) Option 3
758532 There are three events A, B, C, one of which must, and only one can happen, the odds are 8 t0 3 against A, 5 to 2 against B. The odds against C are 43 to 34 32 to 23 34 to 13 None of these Option 1
758633 There are two bags one of which contains 3 black and 4 white balls while other contains 4 black and 4 white balls. A dies is cast, if face 1 or 3 turns up a ball is taken from first bag & if any other face turns up, a ball is chosen from second bag. The probability of choosing of black ball is 11∕21 21/11 12∕21 21/12 Option 1
758734 An urn contains 5 red and 10 black balls. Eight of them are placed in another urn. The chance that the latterthen contains 2 red and 6 black ball is 140/429 129/440 139/420 None of these Option 1
758835 A has one share in a lottery in which there is 1 prize and 2 blanks, B has three shares in a lottery in which there are 3 prizes and 6 blanks, compare probability of A's success to that of B's success is 0.302777778 0.671527778 0.259722222 0.5875 Option 1
758936 If A abd B are independent, then A and ¬B also independent dependent both a & b None of these Option 1
759037 The chance that a leap year selected at random will contain 53 sundays is 7∕2 2∕7 3∕7 None of these Option 2
759138 The set of all possible outcomes is called as event experiment Sample space None of these Option 3
759239 A subset of a sample space is called as event experiment Sample space None of these Option 1
759340 At least one of A or B occur means AUB A∩B AUA None of these Option 1
759441 Both events A & B occur means AUB A∩B AUA None of these Option 1
759542 What is the probability of correctly choosing an unknown integer between 0 to 9 within three chances? 963/1000 973/1000 983/1000 None of these Option 2
759643 A five figure number is formed by the digits 0,1, 2,3,4 without repetition. Then probability that the number formed is divisible by 4 is 3∕15 5∕16 7∕16 9∕16 Option 2
759744 A bag contains 8 white and 6 red balls. The probability of drawing two balls of the same colour is 43/88 43/91 43/93 None of these Option 2
759845 The probability of drawing an ace or a spade or both from a deck of cards is 3∕13 4∕13 4∕17 5∕13 Option 2
759946 If A and B are independent and P(c)= 0, then A, B, & C are independent TRUE FALSE both a & b None of these Option 1
760047 A man alternately tosses a coin & throws a dice, beginning with the coin. Then probability that he will get a head before he gets a 5 or 6 on dice is 1∕4 3∕4 4∕5 4∕7 Option 2
760148 Six dice are thrown simultaneously. The probability that all will show different faces is 5!/65 5!/64 5!/63 None of these Option 2
760249 A box contains 2 white and 4 black balls. Another box B contains 5 white and 7 black balls. A ball is transferred from the box A to the box B. Then a ball is drawn from the box B. The probability that it is white is 16/39 14/39 14580 14489 Option 1
760350 If P(A) >0 , P(B) >0 & P(A/B)= P(B/A), then P(A)= P(B) TRUE FALSE both a & b None of these Option 1
760451 If A & B are possible disjoint, then they are independent TRUE FALSE both a & b None of these Option 2
760552 If a problem in mechanics is given to three students A, B & C whose chances of slogging it are 1/2, 1/3 & 1/4 respectively, then probability that the problem will be solved is 1∕4 4∕5 3∕4 None of these Option 3
760653 A & B throw alternately with a pair of dice. A wins if he throws 6 before B throws 7 & B wins if he throws 7 before A throws 6. If A begins, then his chance of winning is 31/60 30/60 31/61 None of these Option 2
760754 In an experiment a coin is tossed 4 times. What is the size of sample space? 12 14 16 20 Option 3
760855 Three boxes A, B, & C have 1 white, 2 black, 3 red balls, 2 white, 1 black, 1 red balls & 4 white, 5 black, 3 red balls respectively. One box is chosen at randon & two balls are drawn. They happen to be white and red. What is the probability that they come from box B? 50/118 55/118 65/118 None of these Option 2
760956 From a box containing 4 white and 6 black balls, 3 balls are transferred to another empty box. From new box a ball is drawn & it is black. What is the probability that out of 3 balls transferred 2 are white & one black? 1∕4 1∕5 1∕6 1∕7 Option 3
761057 Box A contains three balls with colours red, green & blue & box B contains a balls with colours red, yellow, blue, white & brown. A box is chosen and a ball is picked. What is the probability that a ball may be brown? 1∕10 13∕30 8∕15 None of these Option 1
761158 Box A contains three balls with colours red, green & blue & box B contains a balls with colours red, yellow, blue, white & brown. A box is chosen and a ball is picked. What is the probability that a ball may be green or blue? 1∕11 13∕31 8∕16 None of these Option 2
761259 A committee consists of 9 students two of which are from first year, 3 from second year & 4 from third year. Three students are to be removed at random. What is the probability of the chance that three students belong to different classes ? 3∕7 2∕7 4∕7 5∕7 Option 2
761360 A committee consists of 9 students two of which are from first year, 3 from second year & 4 from third year. Three students are to be removed at random. What is the probability of the chance that two students belong to same class & third to the different class? 55/84 55/85 56/87 57/81 Option 1
7614
7615
7616MCQ 6.1
7617When the possible outcomes of an experiment are equally likely to occur, this we apply:
7618(a) Relative probability (b) Subjective probability
7619(c) Conditional probability (d) Classical probability
7620MCQ 6.2
7621A number between 0 and 1 that is use to measure uncertainty is called:
7622(a) Random variable (b) Trial (c) Simple event (d) Probability
7623MCQ 6.3
7624Probability lies between:
7625(a) -1 and +1 (b) 0 and 1 (c) 0 and n (d) 0 and ∞
7626MCQ 6.4
7627Probability can be expressed as:
7628(a) Ration (b) Fraction (c) Percentage (d) All of the above
7629MCQ 6.5
7630The probability based on the concept of relative frequency is called:
7631(a) Empirical probability (b) Statistical probability (c) Both (a) and (b) (d) Neither (a) nor (b)
7632MCQ 6.6
7633The probability of an event cannot be:
7634(a) Equal to zero (b) Greater than zero (c) Equal to one (d) Less than zero
7635MCQ 6.7
7636A measure of the chance that an uncertain event will occur:
7637(a) An experiment (b) An event (c) A probability (d) A trial
7638MCQ 6.8
7639A graphical device used to list all possibilities of a sequence of outcomes in systematic way is
7640called:
7641(a) Probability histogram (b) Venn diagram (c) Pie diagram (d) Tree diagram
7642MCQ 6.9
7643A random experiment contains:
7644(a) At least one outcome (b) At least two outcomes
7645(c) At most one outcome (d) At most two outcomes
7646MCQ 6.10
7647The probability of all possible outcomes of a random experiment is always equal to:
7648(a) One (b) Zero (c) Infinity (d) All of the above
7649MCQ 6.11
7650The outcome of tossing a coin is a:
7651(a) Mutually exclusive event (b) Compound event (c) Certain event (d) Simple event
7652MCQ 6.12
7653The result of no interest of an experiment is called:
7654(a) Constant (b) Event (c) Failure (d) Success
7655MCQ 6.13
7656A set of all possible outcomes of an experiment is called:
7657(a) Combination (b) Sample point (c) Sample space (d) Compound event
7658MCQ 6.14
7659The numbers of counting rules that are useful in determining the number of outcomes in an
7660experiment are:
7661(a) One (d) Two (c) Three (d) Four
7662MCQ 6.15
7663The events having no experimental outcomes in common is called:
7664(a) Equally likely events (b) Exhaustive events
7665(c) Mutually exclusive events (d) Independent events
7666MCQ 6.16
7667A set of outcomes formed after some additional information is called:
7668(a) Sample space (b) Reduced sample space (c) Null set (d) Random experiment
7669MCQ 6.17
7670The probability associated with the reduced sample space is called:
7671(a) Conditional probability (b) Statistical probability
7672(c) Mathematical probability (d) Subjective probability
7673MCQ 6.18
7674An arrangement of objects without regard to order is called:
7675(a) Permutation (b) Combination (c) Random experiment (d) Sample point
7676MCQ 6.19
7677The number of permutations of a set of n things, taken r at a time with n 2 r given by:
7678MCQ 6.20
7679If three candidates are selected to attend a course from the ten candidates, the number of ways of selecting
7680the candidates is an example of:
7681(a) Combination (b) Permutation (c) Reduced sample space (d) Both (a) and (b)
7682MCQ 6.21
7683When each outcome of a sample space is as likely to occur as any other, the outcomes are called:
7684(a) Exhaustive (b) Mutually exclusive (c) Equally likely (d) Not mutually exclusive
7685MCQ 6.22
7686If A is any event in S and its complement, then P( ) is equal to:
7687(a) 1 (b) 0 (c) 1- A (d) 1 - P(A)
7688MCQ 6.23
7689When certainty is involved in a situation, its probability is equal to:
7690(a) Zero (b) Between -l and + 1 (c) Between 0 and 1 (d) One
7691MCQ 6.24
7692Which of the following cannot be taken as probability of an event?
7693(a) 0 (b) 0.5 (c) 1 (d) -1
7694MCQ 6.25
7695If an event contains more than one sample points, it is called a:
7696(a) Simple event (b) Compound event (c) Impossible event (d) Certain event
7697MCQ 6.26
7698When the occurrence of one event has no effect on the probability of the occurrence of another
7699event, the events are called:
7700(a) Independent (b) Dependent (c) Mutually exclusive (d) Equally likely
7701MCQ 6.27
7702A particular result of an experiment is called:
7703(a) Trial (b) Simple event (c) Compound event (d) Outcome
7704MCQ 6.28
7705A collection of one or more outcomes of an experiment is called:
7706(a) Event (b) Outcome (c) Sample point (d) None of the above
7707MCQ 6.29
7708A process that leads to the occurrence of one and only one of several possible observations is called:
7709(a) Random experiment (c) Random variable (c) Experiment (d) Probability distribution
7710MCQ 6.30
7711Which statement is false?
7712(a) The classical definition applies when there are n equally likely outcomes to an experiment
7713(b) The empirical definition occurs when number of times an event happen is divided by the number
7714of observations.
7715(c) A subjective probability is based on whatever information is available
7716(d) The general rule of addition is used when the events are mutually exclusive
7717MCQ 6.31
7718The term 'sample space' is used for:
7719(a) All possible outcomes (b) All possible coins (c) Probability (d) Sample
7720MCQ 6.32
7721The term 'event' is used for:
7722(a) Time (b) A sub-set of the sample space
7723(c) Probability (d) Total number of outcomes.
7724MCQ 6.33
7725The six faces of the die are called equally likely if the die is:
7726(a) Small (b) Fair (c) Six-faced (d) Round
7727MCQ 6.34
7728If we toss a coin and P(H) = 2P(T), then probability of head is equal to:
7729(a) 0 (b) 1/2 (c) 1/3 (d) 2/3
7730MCQ 6.35
7731A letter is chosen at random from the word "Statistics". The probability of getting a vowel is:
7732(a) 1/10 (b) 2/10 (c) 3/10 (d) 4/10
7733MCQ 6.36
7734An arrangement in which the order of the objects selected from a specific pool of objects is important
7735called:
7736(a) Combination (b) Permutation (c) Factorial (d) Sample space
7737MCQ 6.37
7738Two books are to be selected at random without replacement out of four books. Then number of possible
7739selections are:
7740(a) 4 (b) 2 (c) 6 (d) 3
7741MCQ 6.38
7742Three books of different colours are to be arranged in a book-shelf. The possible arrangements are:
7743(a) 3 (b) 1 (c) 6 (d) 2
7744MCQ 6.39
7745If a sample S = {1, 2}, the number of all possible sub-sets are:
7746(a) 2 (b) 1 (c) 3 (d) 4
7747MCQ 6.40
7748When a die and a coin are rolled together, all possible outcomes are:
7749(a) 6 (b) 2 (c) 36 (d) 12
7750MCQ 6.41
7751When two coins are tossed, the possible outcomes are:
7752(a) 2 (b) 4 (c) 1 (d) None of them
7753MCQ 6.42
7754If three coins are tossed, the possible outcomes are:
7755(a) 8 (b) 3 (c) 1 (d) None of them
7756MCQ 6.43
7757If n coins are tossed, the possible outcomes are:
7758(a) n (b) 2 (c) 2n (d) All of them
7759MCQ 6.44
7760If two dice are roiled, the possible outcomes are:
7761(a) 6 (b) 36 (c) 1 (d) Difficult to answer
7762MCQ 6.45
7763When n dice are rolled, the possible outcomes are:
7764(a) 6n (b) 6 (c) 1 (d) 18
7765MCQ 6.46
7766When one card is selected at random from a pack of 52 playing cards, the possible selections are:
7767(a) 104 (b) 52 (c) 520 (d) 2704
7768MCQ 6.47
7769Two cards are selected at random with replacement from a pack of 52 playing cards. The possible
7770outcomes are:
7771(a) 52 x 52 (b) 52 (c) 1326 (d) 2
7772MCQ 6.48
7773A bag contains 4 white and 2 black balls of the same size and weight, and two balls are selected at
7774random without replacement, the possible selections are:
7775(a) 6 (b) 4 (c) 36 (d) 15
7776MCQ 6.49
7777Two balls are selected at random with replacement from a bag containing 3 red, 3 black and 2 green
7778balls. The possible outcomes are:
7779(a) 8 (b) 64 (c) 16 (d) 2
7780MCQ 6.50
7781Five cards are selected at random from a pack of 52 cards with replacement. The possible
7782combinations are:
7783(a) 52 (b) (52)5 (c) 52 x 52 (d) (5)52
7784MCQ 6.51
7785The digits 1, 2, 3, 4, 5 are the roll numbers of 5 students. These roll numbers are written on the paper
7786slips and two paper slips are selected at random without replacement. The possible combinations are:
7787(a) 5 (b) 2 (c) 25 (d) 10
7788MCQ 6.52
7789Which is the impossible event when a die is rolled:
7790(a) 2 or 3 (b) 5 or 6 (c) 1 (d) 0 or 7
7791MCQ 6.53
7792The probability of drawing any one spade card is:
7793(a) 1/13 (b) 1/4 (c) 4/13 (d) 1/52
7794MCQ 6.54
7795A balance die is rolled, the probability of getting an odd number is:
7796(a) 1/2 (b) 1/4 (c) 1/6 (d) 1/36
7797MCQ 6.55
7798Two fair dice are rolled. The probability of throwing an odd sum is:
7799(a) 1 (b) 1/2 (c) 1/6 (d) 1/36
7800MCQ 6.56
7801Given P(A) = 0.4, P(B) = 0.5 and P(A⋃B)=0.9,then:
7802(a) A and B are not mutually exclusive events (b) A and B are equally likely events
7803(c) A and Bare independent events (d) A and B are mutually exclusive events
7804MCQ 6.57
7805If P(B/A) = 0.50 and P(A⋂B) = 0.40, then p(A) will be equal to:
7806(a) 0.40 (b) 0.50 (c) 0.80 (d) 1
7807MCQ 6.58
7808Which of the following statements is incorrect: ⋃ ⋂ ⋃ ⋂ ⋂ ⋃ ⋂ ⋃
7809MCQ 6.59
7810If P(A/B) = P(A) and P(B/A)=P(B), then A and B are:
7811(a) Mutually exclusive (b) Dependent (c) Equally likely (d) Independent
7812MCQ 6.60
7813A fair coin is tossed 100 times, the expected number of heads is:
7814(a) 100 (b) 50 (c) 30 (d) 60
7815MCQ 6.61
7816When two dice are rolled, the maximum total on the two faces of the dice will be:
7817(a) 6 (b) 36 (c) 12 (d) 2
7818MCQ 6.62
7819A random sample of 200 random digits is selected from a random number table. Expected number of
7820zeros in the sample is:
7821(a) Zero (b) 10 (c) 20 (d) 5
7822MCQ 6.63
7823Six digits are selected at random again and again from a random number table and the even digits are
7824counted each time. In most of the cases, the number of even digits will be:
7825(a) 2 (b) 3 (c) 4 (d) 6
7826MCQ 6.64
7827Two events A and B are called mutually exclusive if:
7828(a) A⋃B = Φ (b) A⋂B = Φ (c) A⋂B = S (d) A⋂B = 1
7829MCQ 6.65
7830If A and B are two mutually exclusive events, then:
7831(a) P(A⋂B) = 0 (b) P(A⋂B) = 1 (c) P(A⋃B) = 0 (d) P(A⋂B) = S
7832MCQ 6.66
7833When A and B are two non-empty and mutually exclusive events, then:
7834(a) P(A⋃B) = P(A).P(B) (b) P(A⋃B) = P(A) + P(B)
7835(c) P(A⋂B) = P(A).P(B) (d) P(A⋂B) = P(A)+P(B)
7836MCQ 6.67
7837The two events A and B are called not mutually exclusive events if:
7838(a) A⋂B = Φ (b) A⋂B ≠ Φ (c) A⋃B = Φ (d) A⋂B = zero
7839MCQ 6.68
7840If A and B are disjoint events then the statement which is always true is:
7841(a) P(A/B) = 0 (b) P(A⋃B) = 0 (c) P(A⋂B) = 1 (d) P(A) = P(B)
7842MCQ 6.69
7843The events A, B and C are called exhaustive events if:
7844(a) A⋃B⋃C = S (b) A⋂B⋂C = S (c) A⋃B⋃C = Φ (d) A⋃B⋃C = Zero
7845MCQ 6.70
7846If A and B are not-mutually exclusive events, then:
7847(a) P(A⋃B) + P(A⋂B) = P(A) + P(B) (b) P(A⋃B) = P(A) + P(B)
7848(c) P(A⋃B) = P(A).P(B) (d) P(A⋂B) = P(A) + P(B)
7849MCQ 6.71
7850If an event is the complement of the event A, then:
7851(a) A⋃ = S (b) A⋂ = S (c) A⋃ = Φ (d) P(A) = P( )
7852MCQ 6.72
7853If A1, A2, A3, ..., Ak are k mutually exclusive events, then:
7854(a) P(A1⋃A2⋃A3⋃ ...⋃Ak ) = P(A1)+P(A2)+P(A3)+...+ P(Ak)
7855(b) P(A1⋃A2⋃A3⋃ ...⋃Ak ) > 1
7856(c) P(A1⋂A2⋂A3⋂ ...⋂Ak ) = 1
7857(d) P(A1⋂A2⋂A3⋂ ...⋂Ak ) = P(A1⋃A2⋃A3⋃ ...⋃Ak )
7858MCQ 6.73
7859If A is an empty set and B is a non-empty set then:
7860(a) A⋂B = S (b) A⋂B = B (c) A⋃B = B (d) P(A) = P(B)
7861MCQ 6.74
7862If A is an empty set and S is the sample space then:
7863(a) P(A⋃S) = P(S) (b) P(A⋃S) = P(Φ) (c) P(A⋂S) = 1 (d) P(A⋃S) = Zero
7864MCQ 6.75
7865If A and B are independent events, then:
7866(a) P(A⋃B) = P(A).P(B) (b) P(A⋂B) = P(A).P(B)
7867(c) P(A⋂B) = P(A)+P(B) (d) P(A) = P(B)
7868MCQ 6.76
7869If A and B are two independent events, then:
7870(a) P(A/B) = P(A) (b) P(A) = P(B) (c) P(A) < P(B) (d) P(A/B) = P(B/A)
7871MCQ 6.77
7872A and B are two independent events. Which one of these equations is false?
7873(a) P(A⋂ ) = P(A)P( ) (b) P( ⋂ ) = P( ⋂ )
7874(c) P( ⋂ ) = P( )P( ) (d) P(A⋃B) = P(A)P(B)
7875MCQ 6.78
7876The conditional probability of the event A when event B has occurred is denoted by:
7877(a) P(A + B) (b) P(A - B) (c) P(A/B) (d) P( )
7878MCQ 6.79
7879If A and B are any two events, then P(A/B)+P( /B) is equal to:
7880(a) 0 (b) 0.25 (c) 0.5 (d) 1
7881MCQ 6.80
7882If A is an arbitrary event, then P(A/A) is equal to :
7883(a) Zero (b) One (c) Infinity (d) Less than one
7884MCQ 6.81
7885If A and B are any two events, then P( /B) is equal to:
7886(a) P(A/B) (b) 1- P(A/B) (c) 1+ P(A/B) (d) P( ⋂B)
7887MCQ 6.82
7888If A and B are any two events, then P(A⋃ ):
7889(a) 1+P(A⋂B) (b) 1-P(A⋃B) (c) 1- P(A⋂B) (d) P(A)+P(B)
7890MCQ 6.83
7891If A and B are any two events, then P( ⋂ ):
7892(a) 1-P(A⋃B) (b) 1-P(A⋂B) (c) 1-P( ⋂B) (d) 1-P(A⋂ )
7893MCQ 6.84
7894Which of the following statements is correct? ⋂ ⋃ ⋂ ⋃ ⋂ ⋃ ⋂ ⋂ ⋂ ⋃ ⋂ ⋂ ⋃ ⋃ ⋂ ⋂ ⋃ ⋂
7895MCQ 6.85
7896If A and B are two mutually exclusive and exhaustive events and P(A)=2P(B), then P(B) is equal to:
7897(a) 1/2 (b) 2/3 (c) 1/3 (d) 1/4
7898MCQ 6.86
7899Two coins are tossed. Probability of getting head on the first coin is:
7900(a) 2/4 (a) 1 (c) Zero (d) 4
7901MCQ 6.87
7902A die and a coin are tossed together. Probability of getting head on the coin is:
7903(a) 6/12 (b) 6 (c) 12 (d) Zero
7904MCQ 6.88
7905A fair die is rolled. Probability of getting even face given that face is less than 5 is given by:
7906(a) 1/2 (b) 5 (c) 2 (d) 6
7907MCQ 6.89
7908Two coins are tossed. The probability that both faces will be matching given by:
7909(a) 1/4 (b) 1/2 (c) 1 (d) Zero
7910MCQ 6.90
7911Two coins are tossed. Probability of getting two heads given that there is at least one head is given
7912by:
7913(a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
7914MCQ 6.91
7915A fair die is rolled. Probability of getting more than4 or less than 3 is given by:
7916(a) 2/3 (b) 1/3 (c) 1/2 (d) 4/3
7917MCQ 6.92
791874. A fair die is rolled. Probability of getting even face or face more than 4 is:
7919(a) 1/3 (b) 2/3 (c) 1/2 (d) 5/6
7920MCQ 6.93
7921Two dice are rolled. Probability of getting similar faces is:
7922(a) 5/36 (b) 1/6 (c) 1/3 (d) 1/2
7923MCQ 6.94
7924Two dice are rolled. Probability of getting total less than 4 or total more than 10 is given by:
7925(a) 10/36 (c) 4/36 (c) 1/36 (d) 14/36
7926MCQ 6.95
7927Two dice are rolled. Probability of getting a total of 4 given that both-faces are similar is:
7928(a) 5/36 (b) 1/36 (c) 4/36 (d) 1/6
7929MCQ 6.96
7930If A and B are two not-independent events, then the probability that both A and B will happen
7931together is:
7932(a) P(A⋂B) = P(A)P(B/A) (b) P(A⋂B) = P(A)P(B)
7933(c) P(A⋂B) = P(A)+P(B) (d) P(A⋂B) = P(A)
7934MCQ 6.97
7935If A and B are two dependent events, then:
7936(a) P(A) P(B/A) = P(B)P(A/B) (b) P(A/B) = P(B/A)
7937(c) P(A/B) = P(A) (d) P(A) = P(B)
7938MCQ 6.98
7939Which one is true?
7940MCQ 6.99
7941(a) 1/5 (b) 2/5 (c) 3/5 (d) 1
7942MCQ 6.100
7943(a) 7/10 (b) 1/10 (c) 3/10 (d) 1
7944MCQ 6.101
7945Given P(A)=2/3, P(B)=3/8 and PAB)=1/4, then A and B are:
7946(a) Independent (b) Dependent (c) Mutually exclusive (d) Equally likely
7947
7948
7949
7950
7951
7952
7953
7954
7955
7956
7957
7958
7959
7960
7961
7962
7963
7964
7965
7966
7967
7968
7969
7970UNIT 4
7971
7972Graph
7973(Q )1 : Graph is collection of ?
7974(A ) points and plane
7975(B ) edges and vertex
7976(C ) edges and weights
7977(D ) vertex and plane
7978(E ) B
7979.
7980(Q ) : An edges whose end vertices are same are called?
7981(A ) self loop
7982(B) parallel edges
7983(C ) circuit
7984(D ) path
7985(E ) A
7986.
7987(Q ) : If more than one edges are associated with a pair of vertex then it is called
7988(A ) parallel edges
7989(B ) self loop
7990(C ) circuit
7991(D ) simple graph
7992(E ) A
7993.
7994(Q ) : A Graph having no parallel edges or self loops are called
7995(A ) Isolated graph
7996(B ) Simple graph
7997(C ) Multi graph
7998(D ) Regular graph
7999(E ) B
8000(Q ) : A graph containing the self loop or parallel edges are called
8001(A ) Simple graph
8002(B ) Multi graph
8003(C ) Regular graph
8004(D ) Path
8005(E ) B
80061
8007(Q ) : The vertex which is not connected to any edges are called
8008(A ) Isolated vertex
8009(B ) Pendant vertex
8010(C ) Adjacent vertex
8011(D ) None of these
8012(E ) A
8013(Q ) : A graph in which all the vertices are of equal degree are called
8014(A ) Regular graph
8015(B ) Multi graph
8016(C ) Simple graph
8017(D ) None of these
8018(E ) A
8019(Q ) : The total number of edges in a complete graph is.
8020(A ) n (n – 1)
8021(B ) n/2
8022(C ) (n – 1)
8023(D ) n (n – 1)/ 2
8024(E ) D
8025(Q ) : The maximum number of edges in any graph is
8026(A ) n (n – 1)
8027(B ) n/2
8028(C ) n (n – 1)/ 2
8029(D ) (n – 1)
8030(E ) C
8031(Q ) : A graph having no edges are called
8032(A ) Isolated graph
8033(B ) Null graph
8034(C ) Regular graph
8035(D ) None
8036(E ) B
8037(Q ) : A vertex with degree one is called
8038(A ) Isolated vertex
80392
8040(B ) Pendant vertex
8041(C ) Adjacent vertex
8042(D ) Null graph
8043(E ) B
8044(Q ) : A subgraph which contains all the vertex of a graph is called
8045(A ) Spanning subgraph
8046(B ) Complement of a graph
8047(C ) Subgraph
8048(D ) None of these
8049(E ) A
8050(Q ) : The number of vertices in a bipartite graph K m, n is
8051(A ) m + n
8052(B ) m ∗ n
8053(C ) m
8054(D ) n
8055(E ) A
8056(Q ) : Total number of edges in a complete bipartite graph K m, n is
8057(A ) m + n
8058(B ) m * n
8059(C ) m
8060(D ) n
8061(E ) B
8062(Q ) : If V 1 is one set of vertex and V 2 is other set of vertex then in case of bipartite graph V 1 ∩ V 2
8063is,
8064(A ) V
8065(B ) V 1
8066(C ) V 2
8067(D ) φ
8068(E ) D
8069(Q ) : If V 1 is one set of vertex and V 2 is other set of vertex then in case of bipartite graph V 1 ∪ V 2
8070is
8071(A ) V
8072(B ) V 1
80733
8074(C ) V 2
8075(D ) φ
8076(E ) A
8077(Q ) : If every edge of one set of vertex is connected with every vertex of other set of vertex then
8078the graph is called
8079(A ) Bipartite graph
8080(B ) Complete bipartite graph
8081(C ) Regular graph
8082(D ) Complete graph
8083(E ) B
8084.
8085(Q ) : If every vertex of graph is adjacent to the all other remaining vertex of graph then it is
8086called
8087(A ) Complete graph
8088(B ) Regular graph
8089(C ) Bipartite graph
8090(D ) None of these
8091(E ) A
8092(Q ) : Maximum degree of a vertex in a simple graph is
8093(A ) n
8094(B ) (n – 1)
8095(C ) n/2
8096(D ) n (n – 1)/ 2
8097(E ) B
8098(Q ) : How many nodes are necessary to construct a graph with exactly 6 edges in which each
8099node is of degree 2 ______ ?
8100(A ) 6
8101(B ) 8
8102(C ) 4
8103(D ) 10
8104(E ) A
8105(Q ) : What is the number of edges in a graph K 10 .
8106(A ) 40
81074
8108(B ) 45
8109(C ) 50
8110(D ) 48
8111(E ) B
8112(Q ) : What is the number of edges in a graph K m, n (K 5, 7 )
8113(A ) 30
8114(B ) 32
8115(C ) 35
8116(D ) 40
8117(E ) C
8118(Q ) : An Isomorphic graph should have
8119(A ) equal number of vertices
8120(B ) equal number of edges
8121(C ) equal number of vertices with a given degree
8122(D ) All the above three
8123(E ) D
8124(Q ) : Whether the graph K 6 and K 3, 3 are Isomorphic or not ?
8125(A ) Yes
8126(B ) No
8127(C )
8128(D )
8129(E )B
8130Explanation :
8131K 6 is a complete graph with n = 6
8132Number of edges = n (n – 1)/2 ⇒ 6 (6 – 1)/ 2 = 15
8133K 3 , 3 is a bipartite graph with number of vertex = 3 + 3 = 6
8134But the number of edges = m * n = 3 + 3 = 9
8135So, K 6 have 15 edges while K 3 , 3 have 9 edges
8136So the given graph is not isomorphic.
8137(Q ) : A spanning subgraph with equal degree of all the vertices are called
8138(A ) factor of a graph
8139(B ) complement of a graph
81405
8141(C ) vertex disjoint subgraph
8142(D ) edge disjoint subgraph
8143(E ) A
81446
8145(Q ) : The minimum number of edges in a connected cyclic graph of n vertices is
8146(A ) n – 1
8147(B ) n
8148(C ) n + 1
8149(D ) None of these
8150(E ) B
8151(Q ) : The number of distinct simple graph with up to 3 node is
8152(A ) 15
8153(B ) 10
8154(C ) 7
8155(D ) 9
8156(E ) C
8157(Q ) : In any undirected graph the sum of degree of all the nodes
8158(A ) must be even
8159(B ) twice the number of edges
8160(C ) must be odd
8161(D ) need not even
8162(E ) B
8163(Q ) : Number of vertices of odd degree in a graph is
8164(A ) always even
8165(B ) always odd
8166(C ) either even or odd
8167(D ) 200
8168(E ) A
8169(Q ) : Maximum degree of any node in a simple graph with n vertices is
8170(A ) n – 1
8171(B ) n
8172(C ) n/2
8173(D ) n – 2
8174(E ) A
8175(Q ) : A given connected graph is Euler graph if and only if all vertices of G are of
8176(A ) same degree
81777
8178(B ) even degree
8179(C ) odd degree
8180(D ) different degree
8181(E ) B
8182(Q ) : A graph is a tree if and only if it is
8183(A ) completely connected
8184(B ) minimally connected
8185(C ) contains circuit
8186(D ) is planar
8187(E ) B
8188(Q ) : A complete graph with n vertices is
8189(A ) 2-chromatic
8190(B ) n/2 chromatic
8191(C ) (n – 1) chromatic
8192(D ) n-chromatic
8193(E ) D
8194(Q ) : The length of a Hamilton path (if exists) in a connected graph of n vertices is
8195(A ) n – 1
8196(B ) n
8197(C ) n + 1
8198(D ) n/2
8199(E ) A
8200(Q ) : T is a graph with n vertices. T is connected and has exactly n – 1 edges then
8201(A ) T is a tree
8202(B ) T contains no cycle
8203(C ) Every pair of vertices in T is connected by exactly one path
8204(D ) Addition of new edge will create a cycle
8205(E ) A
8206Explanation : Theorem
8207(Q ) : A graph can be drawn with 4 edges having vertices of degree.
8208(A ) 4, 3, 2, 1
82098
8210(B ) 3, 2, 1, 0
8211(C ) 4, 5, 6, 7
8212(D ) 3, 2, 2, 1
8213(E ) D
8214(Q ) : What would be the minimum number of edges in a connected graph having 11 vertices.
8215(A ) 5
8216(B ) 10
8217(C ) 15
8218(D ) 20
8219(E ) B
8220(Q ) : Which of the statements are false ?
8221(A ) A graph coursing exists for a graph if the graph has no isolated vertex
8222(B ) No minimal coursing can contain a circuit
8223(C ) A Hamilton circuit is a covering
8224(D ) A spanning tree is covering
8225(A ) c and d
8226(B ) b
8227(C ) a and c
8228(D )None
8229(E ) D
8230(Q ) : Match the list 1 with list II
8231List I List II
8232Hamilton path (i) Contains minimal covering
8233Every covering (ii) Contains every vertex of the graph only once
8234Non-planar graph (iii) Contain K 5 or K 3, 3 as sub-graph
8235(A ) A – 3 b – 1c –2
8236(B ) a – 2 b – 1 c – 3
8237(C ) a – 2 b – 3c – 1
8238(D ) None of these
8239(E ) B
8240(Q ) : The graph Q K
8241(A ) has 2 K vertices
8242(B ) K is regular
82439
8244(C ) Both a and b
8245(D ) None of these
8246(E ) C
8247(Q ) : If G is a planar graph with 35 regions each of degree 6, the number of vertices are,
8248(A ) 70
8249(B ) 80
8250(C ) 72
8251(D ) 62
8252(E ) C
8253(Q ) : Chromatic number of a tree with n vertices is
8254(A ) n – 1
8255(B ) n + 1
8256(C ) 2n
8257(D ) (n/2)
8258(E ) E
825910
8260(Q ) :
8261G 1 G 2 G 3
8262Which of the following is true?
8263(A )G 2 and G 3 are isomorphic
8264(B ) G 1 and G 2 are isomorphic
8265(C ) G 3 is a simple graph
8266(D ) G 1 , G 2 and G 3 are simple graph
8267(E ) B
8268(F
8269(Q ) : Chromatic number of the following graph is
8270(A ) 2
8271(B ) 3
8272(C ) 4
8273(D ) 5
8274(E ) B
8275Fig. Q. 44
8276(Q ) : K n has perfect matching if n is
8277(A ) odd
8278(B ) even
8279(C ) prime
8280(D ) ≥ 4
8281(E ) B
828211
8283(Q ) : Consider the following statement
8284S 1 : A planar graph is 5 colourable
8285S 2 : K n is planar if n ≤ 4
8286(A ) both S 1 and S 2 are true
8287(B ) S 1 is true
8288(C ) S 2 is true
8289(D ) none
8290(E ) C
8291(Q ) : The diameter of the following graph is
8292Fig. Q. 47
8293(A ) 2
8294(B ) 6
8295(C ) 5
8296(D ) 3
8297(E ) D
8298(Q ) : Consider the graph G 1 and G 2
8299G 1 G 2
8300Fig. Q. 48
8301Which of the following is true
8302(A ) G 1 has Euler circuit
8303(B ) G 2 has Euler circuit
8304(C ) Both (A ) and (B ) are valid
830512
8306(D ) None
8307(E ) A
8308(Q ) : If a graph (G) is a connected planar graph with e edge and v vertices where
8309v ≥ 3 then
8310(A ) e = 3 v – 6
8311(B ) e ≤ 3 v – 6
8312(C ) e = 3 v + 6
8313(D ) e ≤ 3 v + 6
8314(E ) B
831513
8316(Q ) : The number of perfect matching in a tree with n vertices is
8317(A ) 2
8318(B ) ≤ 1
8319(C ) n – 1
8320(D )
8321(E ) B
8322(Q ) : Determine the chromatic number of the following graph.
8323Fig. Q. 51
8324(A ) 2
8325(B ) 3
8326(C ) 4
8327(D ) 5
8328(E ) C
8329(Q ) : The chromatic number of a star graph with n vertices is
8330(A ) 2
8331(B ) 4
8332(C ) n – 1
8333(D ) n/2
8334(E ) A
8335(Q ) : Chromatic number of a complete graph K n is
8336(A ) n
8337(B ) n/2
8338(C ) n – 1
8339(D ) n + 1
8340(E ) A
8341(Q ) : Every bipartite graph have the chromatic number
8342(A ) n
834314
8344(B ) n – 1
8345(C ) 2
8346(D ) n/2
8347(E ) C
8348(Q ) : Consider the graph G 1 and G 2
8349G 1 G 2
8350Fig. Q. 55
8351Which of the following is true?
8352(A ) G 2 has Euler path
8353(B ) G 1 has neither Euler circuit nor Euler path
8354(C ) Both (A ) and (B )
8355(D ) None of these
8356(E ) C
8357(Q ) : Consider the graph G 1 and G 2
8358Fig. Q. 56
8359(A ) G 1 has Hamilton circuit
8360(B ) G 2 has Hamilton circuit
8361(C ) Neither G 1 nor G 2 has Hamilton circuit
8362(D ) Both G 1 and G 2 have Hamilton circuit
8363(E ) B
8364(Q ) : What is the height of the given graph ?
836515
8366Fig. Q. 57
8367(A ) 3
8368(B ) 4
8369(C ) 5
8370(D ) 2
8371(E ) B
8372(Q ) : Compare the two figures and conclude
8373Fig. Q. 58
8374(A ) Isomorphic
8375(B ) Not isomorphic as G 2 has no vertex with indegree = 2
8376(C ) Not isomorphic as G 2 has no vertex with outdegree = 2
8377(D ) both (B ) and (C )
8378(E ) D
8379(Q ) : The minimum number of edges in a connected cycle graph of n vertices is
8380(A ) n – 1
8381(B ) n
8382(C ) n + 1
8383(D ) None
8384(E ) B
8385(Q ) : The degree of each reason in a polyhedra graph (degree of each region ≥ 3) with 12
8386vertices and 30 edges is,
8387(A ) 2
838816
8389(B ) 4
8390(C ) 3
8391(D ) 5
8392(E ) C
8393(Q ) : Find the least number of vertices of a complete graph having at least 50 edges.
8394(A ) 25
8395(B ) 20
8396(C ) 15
8397(D ) 10
8398(E ) D
8399(Q ) : A graph needs a chromatic number n. This can be shown by
8400(i) Showing that the graph can be coloured with n colours
8401(ii) Showing that the graph can not be coloured using < n colours
8402(A ) only (i)
8403(B ) only (ii)
8404(C ) (i) and (ii)
8405(D ) None
8406(E ) C
8407(Q ) : Find the chromatic number of the given graph.
8408Fig. Q. 63
8409(A ) 3
8410(B ) 4
8411(C ) 5
8412(D ) 2
8413(E ) B
841417
8415(Q ) : Chromatic number of cycle graph C n , n > 1 and n is odd.
8416(A ) 2
8417(B ) 3
8418(C ) 4
8419(D ) 1
8420(E ) B
8421(Q ) : Chromatic number of cycle graph C n , n > 1 and n is even
8422(A ) 2
8423(B ) 3
8424(C ) 4
8425(D ) 1
8426(E ) A
8427(Q ) : Wheel graph chromatic number ω n , n > 2 if n is odd
8428(A ) 3
8429(B ) 4
8430(C ) 2
8431(D ) 1
8432(E ) A
8433(Q ) : Chromatic number of a wheel graph ω n , n > 2 if n is even
8434(A ) 1
8435(B ) 3
8436(C ) 4
8437(D ) 2
8438(E ) C
8439(Q ) : A graph which consists of only isolated vertex has chromatic number.
8440(A ) 2
844118
8442(B ) 1
8443(C ) 3
8444(D ) None of these
8445(E ) B
8446(Q ) : A graph has one or more edges (without self loop) has a minimum chromatic number ?
8447(A ) 2
8448(B ) 3
8449(C ) 4
8450(D ) 1
8451(E ) A
8452(Q ) : Every tree with two or more vertex has chromatic number.
8453(A ) 1
8454(B ) 2
8455(C ) 4
8456(D ) 3
8457(E ) B
8458(Q ) : A graph has chromatic number 2 if and only if it has no circuits of odd length.
8459(A ) True
8460(B ) False
8461(E ) A
8462Ans. : (A )
8463(Q ) : If d is the maximum degree of the vertices in the graph G then chromatic number of G is
8464(A ) ≤ d + 1
8465(B ) ≥ d + 1
8466(C ) ≤ d – 1
8467(D ) ≥ d – 1
8468(E ) A
8469(Q ) : The minimum number of edges in a connected graph with n vertices
8470(A ) n – 1
8471(B ) n
8472(C ) n + 1
8473(D ) None of these
8474(E ) A
847519
8476(Q ) : A graph is planar if and only if it does not contain
8477(A ) Subgraph homeomorphic to K 3 and K 3, 3
8478(B ) Subgraph isomorphic to K 5 or K 3, 3
8479(C ) Subgraph isomorphic to K 3 and K 3, 3
8480(D ) Subgraph homeomorphic to K 5 or K 3, 3
8481(E ) D
8482(Q ) : Maximum number of edges in a n-node undirected graph without self loop is
8483(A ) n 2
8484(B )
8485(C ) n – 1
8486(D )
8487(E ) B
8488(Q ) : The vertex connectivity of K 5 is,
8489(A ) 2
8490(B ) 3
8491(C ) 4
8492(D ) 1
8493(E ) C
8494(Q ) : If every edge of the graph G appears exactly once in the path then it is
8495(A ) Hamilton path
8496(B ) Eulerian path
8497(C ) Simple path
8498(D ) Shortest path
8499(E ) B
8500(Q ) : If a graph possesses either zero or two vertices of odd degree then it is
8501(A ) Hamilton path
8502(B ) Eulerian path
8503(C ) Simple path
8504(D ) Shortest path
8505(E ) E
850620
8507(Q ) : A connected graph having the degree of all vertices is even then it contains
8508(A ) Hamilton circuit
8509(B ) Simple circuit
8510(C ) Eulerian circuit
8511(D ) None of these
8512(E ) C
8513(Q ) : A directed graph possesses an Eulerian circuit if it is connected and the
8514(A ) Incoming degree = outgoing degree
8515(B ) Incoming degree ≠ outgoing degree
8516(C ) Incoming degree > outgoing degree
8517(D ) Incoming degree < outgoing degree
8518(E ) A
8519(Q ) : If every vertex of a graph is appearing exactly once then it is
8520(A ) Hamilton path
8521(B ) Eulerian path
8522(C ) Simple path
8523(D ) Shortest path
8524(E ) A
8525(Q ) : If G be a simple connected graph and sum of the degree of each pair of vertex ≥ (n – 1)
8526then it contains
8527(A ) Eulerian path
8528(B ) Hamilton path
8529(C ) Simple path
8530(D ) None
8531(E ) B
8532(Q ) : For a connected graph having Hamilton circuit, which condition to be satisfied
8533(A ) degree of each vertex = n – 1
8534(B ) degree of each vertex = n
8535(C ) d (v) ≥ n/2
8536(D ) d (v) = n + 1
8537(E ) C
8538(Q ) : A simple graph in which there exists an edge between every pair of vertex is called
853921
8540(A ) Complete graph
8541(B ) Euler graph
8542(C ) Plannar graph
8543(D ) Regular graph
8544(E ) A
8545(Q ) : The minimum number of spanning tree in a connected graph with n node is,
8546(A ) 1
8547(B ) 2
8548(C ) n – 1
8549(D ) n/2
8550(E ) B
8551(Q ) : If a graph require k different colours for its proper colouring. Then chromatic
8552number of the graph is,
8553(A ) 1
8554(B ) k
8555(C ) k – 1
8556(D ) k/2
8557(E ) B
8558(Q ) : The number of colours required to properly colour the vertices of every planar graph is
8559(A ) 2
8560(B ) 3
8561(C ) 4
8562(D ) 5
8563(E ) A
8564(Q ) : Degree of each vertex in K n is,
8565(A ) n
8566(B ) n – 1
8567(C ) n – 2
8568(D ) 2n – 1
8569(E ) B
8570(Q ) : Common data for Q. 90 to 92 Vertex V 6 is called
857122
8572Fig. Q. 89
8573(A ) Pendant vertex
8574(B ) Isolated vertex
8575(C ) Incident vertex
8576(D ) Adjacent vertex
8577(E ) B
8578(Q ) : Vertex V 5 is called
8579(A ) Pendant
8580(B ) Isolated
8581(C ) Adjacent
8582(D ) Incident
8583(E ) A
8584(Q ) : Edge e 4 is called
8585(A ) Self loop
8586(B ) Parallel edge
8587(C ) Incident
8588(D ) None
8589(E ) B
8590(Q ) : edge e 6 is called
8591(A ) Parallel edge
8592(B ) Self loop
8593(C ) Incident edge
8594(D ) None
8595(E ) B
8596(Q ) : In a graph G d (V i ) = ?
859723
8598(A ) e
8599(B ) 2e
8600(C ) e/2
8601(D ) 3e
8602(E ) B
8603(Q ) : The number of vertices of odd degree in a graph is always.
8604(A ) Odd
8605(B ) Even
8606(C ) 2e
8607(D ) None
8608(E ) B
8609(Q ) : How many nodes are required to construct a graph with exactly 6 edges in which each
8610node is of degree 2.
8611(A ) 4
8612(B ) 7
8613(C ) 6
8614(D ) 8
8615(E ) C
8616(Q ) : What is the number of edges in a graph with 6 nodes, 2 of degree 4 and 4 of degree 2.
8617(A ) 6
8618(B ) 8
8619(C ) 7
8620(D ) 5
8621(E ) B
8622(Q ) : Whether K 6 and K 3, 3 are isomorphic ?
8623(A ) True
8624(B ) False
8625(E ) B
8626(Q ) :
862724
8628Fig. Q. 98
8629G 1 and G 2 are isomorphic
8630(A ) True
8631(B ) False
8632(E ) A
8633(Q ) : Does the graph K 1, 3 have Eulerian circuit ?
8634(A ) Yes
8635(B ) No
8636(E ) B
8637(Q ) : How many edges must a planar graph have if it has 7 regions and 5 nodes?
8638(A ) 8
8639(B ) 10
8640(C ) 12
8641(D ) 14
8642(E ) B
8643(Q ) : How many number of regions defined by a connected planar graph with 6 nodes and 10
8644edges.
8645(A ) 4
8646(B ) 6
8647(C ) 8
8648(D ) 10
8649(E ) B
8650(Q ) : A connected planar graph has nine vertices having degree 2, 2, 2, 2, 3, 3, 3, 4, 4, and 5.
8651How many edges are there ?
8652(A ) 10
8653(B ) 12
8654(C ) 14
865525
8656(D ) 16
8657(E ) C
8658(Q ) : In the same problem as in Q 102, how many regions ?
8659(A ) 4
8660(B ) 6
8661(C ) 7
8662(D ) 8
8663(E ) C
8664(Q ) : Let G1 be a simple connected planar graph with 13 vertices and 19 edges. Thus the
8665number of faces in the planner graph is
8666(A ) 6
8667(B ) 8
8668(C ) 9
8669(D ) 13
8670(E ) B
8671(Q ) : The maximum no. of edges in a planar graph is
8672(A ) 3V – 6
8673(B ) 2 V – 4
8674(C ) 2e
8675(D ) None
8676(E ) A
8677(Q ) : The number of connected component in G is
8678(A ) n
8679(B ) n + 2
8680(C ) 2 n/2
8681(D ) 2 n / n
8682(E ) B
8683(Q ) : Which of the following graph has an Eulerian circuit ?
8684(A ) Any k-regular graph where K is an even numbers.
8685(B ) A complete graph on 90 vertices.
8686(C ) The complement of a cycle on 25 vertices.
8687(D ) None of these
868826
8689(E ) A
8690(Q ) : Which of the following statements in true for every planar graph on n vertices.
8691(A ) The graph is connected
8692(B ) The graph is Eulerian
8693(C ) The graph has vertex-cover of size at most 3n/4
8694(D ) The graph has an independent set of size at least n/3.
8695(E ) A
8696(Q ) : What is the number of vertices in an undirected graph with 27 edges, 6 vertices of degree
86972, 3 vertices of degree 4 and remaining of degrees 3 ?
8698(A ) 10
8699(B ) 11
8700(C ) 18
8701(D ) 19
8702(E ) D
8703(Q ) : Consider the graph shown below. The vertex connectivity of the graph is
8704Fig. Q. 110
8705(A ) 1
8706(B ) 2
8707(C ) 3
8708(D ) 4
8709(E ) B
8710(Q ) : Consider the graph shown below. The edge connectivity of the graph is
871127
8712Fig. Q. 111
8713(A ) 1
8714(B ) 2
8715(C ) 3
8716(D ) 4
8717(E ) A
8718(Q ) : The edge connectivity for the complete graph K 6 is
8719(A ) 5
8720(B ) 3
8721(C ) 2
8722(D ) 4
8723(E ) A
8724(Q ) : The vertex connectivity for the complete bipartite graph K 3 , 4 is
8725(A ) 1
8726(B ) 4
8727(C ) 3
8728(D ) 2
8729(E ) C
8730(Q ) : A graph which has an Hamilton circuit is called
8731(A ) Hamilton graph
8732(B ) Complete bipartite graph
8733(C ) Eulurian graph
8734(D ) None of these
8735(E ) A
8736(Q ) : The complete bipartite graph K 2 , 4 has
8737(A ) Eulurian circuit
8738(B ) Hamilton circuit
873928
8740(C ) neither eulurian nor Hamilton circuit
8741(D ) both eulurian nor Hamilton circuit
8742(E )
8743Ans. : (**)
8744(Q ) : Consider the following graph. It has
8745(A ) Eulurian circuit
8746(B ) Hamilton circuit
8747(C ) both Fig. Q. 116
8748(D ) neither
8749(E ) B
8750(Q ) : Consider the following graph. It has
8751(A ) Eulurian circuit
8752(B ) Hamilton circuit Fig. Q. 117
8753(C ) both
8754(D ) neither
8755(E ) D
8756(Q ) : The minimum number of colors required to produce a proper coloring of a simple
8757connected graph G is called
8758(A ) chromatic number of G
8759(B ) edge connectivity of G.
8760(C ) Vertex connectivity of G
8761(D ) none of these
8762(E ) A
8763(Q ) : If a graph G is isomorphic to its complement then G is called
8764(A ) complete graph
8765(B ) bipartite graph
8766(C ) Self complementary graph
8767(D ) None of these
8768(E ) C
876929
8770(Q ) : Consider the graph G 1 and G 2 below. Then G 1 U G 2 is
8771Fig. Q. 120
8772(A )
8773(B )
8774(C )
8775(D )
8776(E ) B
8777(Q ) : In the previous quertion G 1 n G 2 is
8778(A )
8779(B )
878030
8781(C )
8782(D )
8783(E ) C
8784(Q ) : Consider the following graph, the vertex connectivity is
8785(A ) 1
8786(B ) 2
8787(C ) 4
8788(D ) 3
8789(E ) B
8790Fig. Q. 122
8791(Q ) : Consider the following graph and find the edge connectivity of the graph
8792(A ) 1
8793(B ) 3
8794(C ) 2
8795(D ) 4
8796(E ) B
8797Fig. Q. 123
879831
8799(Q ) : Consider the graph G 1 and its subgraph G 2 .
8800Fig. Q. 124
8801Then subgraph G 2 is called
8802(A ) complete subgraph
8803(B ) regular subgraph
8804(C ) spanning subgraph
8805(D ) none of these
8806(E ) C
8807(Q ) : Consider the graph G and its subgraph H 1 and H 2 .
8808Fig. Q. 125
8809Then H 1 and H 2 are.
881032
8811(A ) Vertex disjoint subgraph
8812(B ) spanning subgraphs
8813(C ) Regular subgraphs
8814(D ) none of these
8815(E ) A
8816(Q ) : Consider the following graph G and its subgraph H 1 and H 2 .
8817Fig. Q. 126
8818Then H 1 and H 2 are.
8819(A ) vertex disjoint
8820(B ) edge disjoint
8821(C ) spanning
8822(D ) none of these
8823(E ) B
8824(Q ) : The adjacency matrix for the following graph is
8825Fig. Q. 127
8826(A )
8827(B )
8828(C )
8829(D )
883033
8831(E ) A
883234
8833(Q ) : If G is a simple graph on n vertices and the degree of each vertex is
8834(n – 1) then the graph is :
8835(A ) bipartite graph
8836(B ) null graph
8837(C ) complete graph
8838(D ) None of these
8839(E ) C
8840(Q ) : In the following graph, the adjacent vertex are :
8841(A ) e 1 and e 3
8842(B ) e 2 and e 5
8843(C ) e 1 and e 4
8844(D ) None of these
8845(E ) B
8846Fig. Q. 129
8847(Q ) : In the following graph, the adjacent vertex are
8848(A ) v 1 and v 2
8849(B ) v 2 and v 4
8850(C ) v 1 and v 3
8851(D ) None of these
8852(E ) A
8853Fig. Q. 130
8854-----------------------------------------------------------------------------------------------------------------------------------------
8855(Q)2: In the following graph, the adjacent vertices are
885635
8857(A) v1, v3
8858(B)v2, v4
8859(C)v2, v3
8860(D)v3, v4
8861(E) C
8862(Q)2: In the following graph, the pendant vertices are
8863(A)v1
8864(B)v1, v2
8865(C)v2
8866(D)v3, v4
8867(E)D
8868(Q)2: The Directed graph G is shown below .The indegree of vertex of v1 is
886936
8870(A)1
8871(B)2
8872(C)3
8873(D)4
8874(E) B
8875(Q)1: A vertex of degree zero in a graph is called
8876(A)pendant vertex
8877(B)isolated vertex
8878(C)adjacent vertex
8879(D) none of these
8880(E)B
8881(Q)1:A graph without selfloop without edges is known as………..
8882(A) multiple graph
8883(B) simple graph
8884(C) weighted graph
8885(D) none of these
8886(E) B
888737
8888(F) .
8889(Q)2: The number of edges in a graph with 6 nodes in which 2 nodes are of degree 4 and remaining
8890nodes of degree 2 is
8891(A)7
8892(B)8
8893(C)6
8894(D)5
8895(E) B
8896(Q)2:The number of nodes required to construct a graph with exactly 8 edges in which each nodes is
8897of degree 2 is…………
8898(A)8
8899(B)7
8900(C)6
8901(D)5
8902(E) A
8903(Q)2: If G is a simple graph on n vertices and the degree of each vertex is (n-1) then the graph is
8904(A)bipartite graph
8905(B)null graph
8906(C)complete graph
8907(D)none of these
8908(E) C
890938
8910(Q)2: Consider the following graphs G1 and G2, then graphs are
8911(A) complete graphs
8912(B) isomorphic graphs
8913(C) null graphs
8914(D) non isomorphic graphs
8915(E) B
8916(F) .
8917(Q)2): The complete graph on 3 vertices is also a
8918(A) regular graph
8919(B) bipartite graph
8920(C)null graph
8921(D)none of these
8922(E) A
8923(F) .
8924(Q)2: The number of edges, the complete graph k 5 has
8925(A) 5
8926(B) 6
8927(C) 9
8928(D) 10
892939
8930(E) D
8931(F) .
8932(Q)2:Consider the following graph G and its subgraphs H1 and H2, Then H1 and H2 are
8933(A) vertex disjoint subgraphs
8934(B) edge disjoint subgraphs
8935(C) spanning subgraphs
8936(D)none of these
8937(E) B
8938(Q)2: Consider the graph G and its subgraph H, then subgraph H is a
8939(A) complete sub-graph
894040
8941(B) regular sub-graph
8942(C) spanning subgraph
8943(D) none of these
8944(E) C
8945(F) .
8946(Q)2: If a graph G is isomorphic to its complement then G is called
8947(A) complete graph
8948(B) bipartite graph
8949(C) self complementary graph
8950(D) none of these
8951(E) C
8952(F) .
8953(Q)1: The edge connectivity for the complete graph k6 on six vertices is
8954(A)3
8955(B)5
8956(C)4
8957(D)2
8958(E) B
8959(F)
8960(Q)1:A circuit which contains every edge of the graph appears exactly once, is called
8961(A)Hamiltonian path
8962(B) Eulerian path
8963(C) Hamiltonian circuit
8964(D) none of these
8965(E) B
8966(F)
896741
8968(Q):A circuit which contains every edge of the graph exactly once is called
8969(A) Eulerian circuit
8970(B) Hamiltonian circuit
8971(C) Hamiltonian path
8972(D) none of these
8973(E) A
8974(F)
8975(Q)1: A graph possesses an Eulerian circuit if and only if it is connected and has vertices which all
8976have
8977(A) even edges
8978(B) odd edges
8979(C) degree one
8980(D) degree three
8981(E) A
8982(Q)1: A graph which has an Hamiltonian circuit is called
8983(A) Hamiltonian graph
8984(B) complete bipartite graph
8985(C) Eulerian graph
8986(D) none of these
8987(E) A
8988(Q)1:The complete bipartite graph K23 has
8989(A) Eulerian circuit
8990(B) Hamiltonian circuit
8991(C) both Eulerian and Hamiltonian circuit
8992(D) neither Eulerian and Hamiltonian circuit
899342
8994(E) D
8995(Q):Consider the following graph. It has
8996(A) Eulerian circuit
8997(B) Hamiltonian circuit
8998(C) neither Eulerian and Hamiltonian circuit
8999(D) both Eulerian and Hamiltonian circuit
9000(E) B
9001(F)
9002(Q)1:A Graph which can be drawn on the plane such that no edges cross each other,is
9003called
9004(A) planar graph
9005(B) complete graph
9006(C) complete bipartite graph
9007(D) none of these
9008(E) A
9009(F)
9010(Q)1: How many edges must a planar graph have if it has 7 regions and 5 vertices ?
9011(A)9
9012(B)10
9013(C)8
9014(D)7
9015(E) B
9016(F)
9017(Q)2: A connected planar graph has nine vertices having degree 2, 2, 2, 3, 3, 3, 4, 4 and 5.
9018The number of region s it has is
901943
9020(A) 6
9021(B) 5
9022(C) 7
9023(D) 9
9024(E) C
9025(F)
9026(Q)2: The minimum number of colours needed to produce a proper colouring of a simple connected
9027graph G is called
9028(A) chromatic number of G
9029(B) edge connectivity of G
9030(C) vertex connectivity of G
9031(D) none of these
9032(E) A
9033(F)
9034(Q)2: The chromatic number of complete bipartite graph K m,n is
9035(A) m
9036(B) n
9037(C) 2
9038(D) 1
9039(E) C
9040(F)
9041(Q): The chromatic number of the following graph is .
9042(A) 3
9043(B) 2
9044(C) 4
9045(D) 7
9046(E) A
9047
9048
9049((MARKS)) (1/2/3...) 2
9050((QUESTION)) If self loops as well as parallel edges are allowed, the graph is known as ____.
9051((OPTION_A)) multigraph
9052((OPTION_B)) pseudograph
9053((OPTION_C)) simple graph
9054((OPTION_D)) none of these
9055((CORRECT_CHOICE)) (A/B/C/D) B
9056((EXPLANATION)) (OPTIONAL)
9057
9058
9059((MARKS)) (1/2/3...) 2
9060((QUESTION)) If no self loop and no parallel edges are present in a graph, the graph is known as ___ .
9061((OPTION_A)) multigraph
9062((OPTION_B)) pseudograph
9063((OPTION_C)) simple graph
9064((OPTION_D)) none of these
9065((CORRECT_CHOICE)) (A/B/C/D) C
9066((EXPLANATION)) (OPTIONAL)
9067
9068
9069((MARKS)) (1/2/3...) 2
9070((QUESTION)) If parallel edges are allowed but self loops are not permitted, the graph is known as ___.
9071((OPTION_A)) multigraph
9072((OPTION_B)) pseudograph
9073((OPTION_C)) simple graph
9074((OPTION_D)) none of these
9075((CORRECT_CHOICE)) (A/B/C/D) a
9076((EXPLANATION)) (OPTIONAL)
9077
9078
9079((MARKS)) (1/2/3...) 2
9080((QUESTION)) In a graph the number of vertices of odd degree is ___.
9081((OPTION_A)) Odd
9082((OPTION_B)) Even
9083((OPTION_C)) zero
9084((OPTION_D)) none of these
9085((CORRECT_CHOICE)) (A/B/C/D) b
9086((EXPLANATION)) (OPTIONAL)
9087
9088((MARKS)) (1/2/3...) 2
9089((QUESTION)) How many nodes are necessary to construct a graph with exactly 8 edges in which each node is of degree 2?
9090((OPTION_A)) 2
9091((OPTION_B)) 4
9092((OPTION_C)) 8
9093((OPTION_D)) 16
9094((CORRECT_CHOICE)) (A/B/C/D) c
9095((EXPLANATION)) (OPTIONAL)
9096
9097
9098((MARKS)) (1/2/3...) 2
9099((QUESTION)) The sum of the degrees of the vertices of the graph is___.
9100((OPTION_A)) same as no. of edges
9101((OPTION_B)) twice the no. of edges
9102((OPTION_C)) half the no. of edges
9103((OPTION_D)) none of these
9104((CORRECT_CHOICE)) (A/B/C/D) b
9105((EXPLANATION)) (OPTIONAL)
9106
9107
9108
9109((MARKS)) (1/2/3...) 2
9110((QUESTION)) Degree of any vertex of a simple graph with n vertices is at the most__.
9111((OPTION_A)) n
9112((OPTION_B)) n+1
9113((OPTION_C)) n-1
9114((OPTION_D)) 2n
9115((CORRECT_CHOICE)) (A/B/C/D) c
9116((EXPLANATION)) (OPTIONAL)
9117
9118 1) 2) 3) 2n 4) n(n - 1) / 2 4
9119
9120((MARKS)) (1/2/3...) 2
9121((QUESTION)) Maximum number of edges in a simple graph with n vertices is__.
9122((OPTION_A)) n(n+1) / 2
9123((OPTION_B)) n
9124((OPTION_C)) 2n
9125((OPTION_D)) n(n - 1) / 2
9126((CORRECT_CHOICE)) (A/B/C/D) d
9127((EXPLANATION)) (OPTIONAL)
9128
9129
9130((MARKS)) (1/2/3...) 2
9131((QUESTION)) Determine the number of edges in a graph with 6 nodes, 2 vertices of degree 4 and 4 vertices of degree 2.
9132((OPTION_A)) 4
9133((OPTION_B)) 8
9134((OPTION_C)) 2
9135((OPTION_D)) 16
9136((CORRECT_CHOICE)) (A/B/C/D) b
9137((EXPLANATION)) (OPTIONAL)
9138
9139
9140((MARKS)) (1/2/3...) 2
9141((QUESTION)) An a directed graph, e is an edge from a to b then _____.
9142((OPTION_A)) a is known as initial vertex and b is not a terminal vertex
9143((OPTION_B)) a is not initial vertex and b is a terminal vertex.
9144((OPTION_C)) a is not initial vertex and b is not a terminal vertex
9145((OPTION_D)) a is initial vertex and b is a terminal vertex.
9146((CORRECT_CHOICE)) (A/B/C/D) d
9147((EXPLANATION)) (OPTIONAL)
9148
9149
9150((MARKS)) (1/2/3...)
9151((QUESTION)) A graph with n vertices is a complete graph if ____.
9152((OPTION_A)) degree of each vertex is n
9153((OPTION_B)) degree of each vertex is (n – 1)
9154((OPTION_C)) degree of each vertex is (n + 1)
9155((OPTION_D)) degree of each vertex is 2n
9156((CORRECT_CHOICE)) (A/B/C/D) b
9157((EXPLANATION)) (OPTIONAL)
9158
9159
9160
9161((MARKS)) (1/2/3...) 2
9162((QUESTION)) No. of edges in a complete graph Kn is ____.
9163((OPTION_A)) n
9164((OPTION_B)) n^2
9165((OPTION_C)) n(n - 1) / 2
9166((OPTION_D)) n(n + 1) /2
9167((CORRECT_CHOICE)) (A/B/C/D) c
9168((EXPLANATION)) (OPTIONAL)
9169
9170
9171((MARKS)) (1/2/3...) 2
9172((QUESTION)) Which is true?
9173((OPTION_A)) complete graph <=> regular graph
9174((OPTION_B)) complete graph => regular graph but converse need not be true
9175((OPTION_C)) regular graph => complete graph but converse need not be true
9176((OPTION_D)) none of these
9177((CORRECT_CHOICE)) (A/B/C/D) B
9178((EXPLANATION)) (OPTIONAL)
9179
9180
9181
9182((MARKS)) (1/2/3...) 2
9183((QUESTION)) A complete bipartite graph Km,n is regular if____.
9184((OPTION_A)) m > n
9185((OPTION_B)) m < n
9186((OPTION_C)) m=n
9187((OPTION_D)) None of these
9188((CORRECT_CHOICE)) (A/B/C/D) C
9189((EXPLANATION)) (OPTIONAL)
9190
9191
9192((MARKS)) (1/2/3...) 2
9193((QUESTION)) How many edges K6 (complete graph with 6 vertices) has?
9194((OPTION_A)) 30
9195((OPTION_B)) 15
9196((OPTION_C)) 6
9197((OPTION_D)) 21
9198((CORRECT_CHOICE)) (A/B/C/D) B
9199((EXPLANATION)) (OPTIONAL)
9200
9201((MARKS)) (1/2/3...) 2
9202((QUESTION)) How many edges K4,6 has ?
9203((OPTION_A)) 24
9204((OPTION_B)) 10
9205((OPTION_C)) 12
9206((OPTION_D)) 15
9207((CORRECT_CHOICE)) (A/B/C/D) a
9208((EXPLANATION)) (OPTIONAL)
9209
9210
9211((MARKS)) (1/2/3...) 2
9212((QUESTION)) Which graph is complete bipartite graph but not a regular graph ?
9213((OPTION_A)) K3,3
9214((OPTION_B)) K4,4
9215((OPTION_C)) K1,6
9216((OPTION_D)) none of these
9217((CORRECT_CHOICE)) (A/B/C/D) c
9218((EXPLANATION)) (OPTIONAL)
9219
9220
9221((MARKS)) (1/2/3...) 2
9222((QUESTION)) If G is graph whosw set of vertices is V. If V can b partitioned into two subsets V1 and V2 such that every edge of G joins V1 with V2 also V1 U V2 =V and V1
9223((OPTION_A)) G is a regular graph
9224((OPTION_B)) G is a bipartite graph
9225((OPTION_C)) G is a complete graph
9226((OPTION_D)) none of these
9227((CORRECT_CHOICE)) (A/B/C/D) B
9228((EXPLANATION)) (OPTIONAL)
9229
9230((MARKS)) (1/2/3...) 2
9231((QUESTION)) A vertex with degree zero is known as __.
9232((OPTION_A)) Pendant vertex
9233((OPTION_B)) isolated vertex
9234((OPTION_C)) node
9235((OPTION_D)) junction
9236((CORRECT_CHOICE)) (A/B/C/D) b
9237((EXPLANATION)) (OPTIONAL)
9238
9239((MARKS)) (1/2/3...) 2
9240((QUESTION)) A vertex with degree one is known as __.
9241((OPTION_A)) Pendant vertex
9242((OPTION_B)) isolated vertex
9243((OPTION_C)) node
9244((OPTION_D)) junction
9245((CORRECT_CHOICE)) (A/B/C/D) A
9246((EXPLANATION)) (OPTIONAL)
9247
9248((MARKS)) (1/2/3...) 2
9249((QUESTION)) How many nodes are necessary to construct a graph with exactly n edges in which each node is of degree 2?
9250((OPTION_A)) n-1
9251((OPTION_B)) n
9252((OPTION_C)) n +1
9253((OPTION_D)) 2n
9254((CORRECT_CHOICE)) (A/B/C/D) b
9255((EXPLANATION)) (OPTIONAL)
9256
9257((MARKS)) (1/2/3...) 2
9258((QUESTION)) A graph is known as null graph if__.
9259((OPTION_A)) it has no edges
9260((OPTION_B)) it has no vertices
9261((OPTION_C)) it has no edges and no vertices
9262((OPTION_D)) none of these
9263((CORRECT_CHOICE)) (A/B/C/D) a
9264((EXPLANATION)) (OPTIONAL)
9265
9266
9267((MARKS)) (1/2/3...) 2
9268((QUESTION)) A graph with 4 nodes and 7 edges can not be a__.
9269((OPTION_A)) multigraph
9270((OPTION_B)) pseudograph
9271((OPTION_C)) simple graph
9272((OPTION_D)) all of these
9273((CORRECT_CHOICE)) (A/B/C/D) c
9274((EXPLANATION)) (OPTIONAL)
9275
9276
9277((MARKS)) (1/2/3...) 2
9278((QUESTION)) A subgraph G' of G is known as spanning subgraph if__.
9279((OPTION_A)) G' contains all the edges of G
9280((OPTION_B)) G' contains all the vertices of G
9281((OPTION_C)) both (a) and (b)
9282((OPTION_D)) none of these
9283((CORRECT_CHOICE)) (A/B/C/D) b
9284((EXPLANATION)) (OPTIONAL)
9285
9286((MARKS)) (1/2/3...) 2
9287((QUESTION)) Two graphs G1 and G2 are isommorphic if__.
9288((OPTION_A)) number of vertices as well as edges in G1 and G2 are same
9289((OPTION_B)) G1 has n vertices of degree k then G2 must have exactly n vertices of degree k
9290((OPTION_C)) adjacency is preserved
9291((OPTION_D)) all of these
9292((CORRECT_CHOICE)) (A/B/C/D) d
9293((EXPLANATION)) (OPTIONAL)
9294
9295
9296((MARKS)) (1/2/3...) 2
9297((QUESTION)) Under which condition Km,n , the complete bipartite graph will have an Eulerian circuit ?
9298((OPTION_A)) If m = n and both are odd
9299((OPTION_B)) If m != n and either m is odd or n is odd
9300((OPTION_C)) If both m and n are even (m = n or m != n)
9301((OPTION_D)) none of these
9302((CORRECT_CHOICE)) (A/B/C/D) c
9303((EXPLANATION)) (OPTIONAL)
9304
9305((MARKS)) (1/2/3...) 2
9306((QUESTION)) An undirected graph possesses an Eulerian path if__.
9307((OPTION_A)) it is connected and has either zero or two vertices of odd degree
9308((OPTION_B)) it is connected and has even no. of vertices (> 2) of odd degree
9309((OPTION_C)) both (a) and (b)
9310((OPTION_D)) none of these
9311((CORRECT_CHOICE)) (A/B/C/D) a
9312((EXPLANATION)) (OPTIONAL)
9313
9314((MARKS)) (1/2/3...) 2
9315((QUESTION)) An undirected graph possesses an Eulerian circuit if__.
9316((OPTION_A)) it is connected and has two vertices of odd degrees
9317((OPTION_B)) it is connected and its vertices are all of even degree
9318((OPTION_C)) both (a) and (b)
9319((OPTION_D)) none of these
9320((CORRECT_CHOICE)) (A/B/C/D) B
9321((EXPLANATION)) (OPTIONAL)
9322
9323((MARKS)) (1/2/3...) 2
9324((QUESTION)) A graph is known as Eulerian path if __.
9325((OPTION_A)) every vertex of the graph G appears exactly once in the path
9326((OPTION_B)) every edge of the graph G appears exactly once in the path
9327((OPTION_C)) both (a) and (b)
9328((OPTION_D)) none of these
9329((CORRECT_CHOICE)) (A/B/C/D) b
9330((EXPLANATION)) (OPTIONAL)
9331
9332
9333((MARKS)) (1/2/3...) 2
9334((QUESTION)) A path in a connected graph G is Hamiltonian path if__.
9335((OPTION_A)) It contains every edge of G exactly once
9336((OPTION_B)) It contains every vertex of G exactly once
9337((OPTION_C)) both (a) and (b)
9338((OPTION_D)) none of these
9339((CORRECT_CHOICE)) (A/B/C/D) B
9340((EXPLANATION)) (OPTIONAL)
9341
9342((MARKS)) (1/2/3...) 2
9343((QUESTION)) How many Hamiltonian circuits exists in Kn ?
9344((OPTION_A)) N
9345((OPTION_B)) n-1
9346((OPTION_C)) n(n - 1) / 2
9347((OPTION_D)) (n - 1)! / 2
9348((CORRECT_CHOICE)) (A/B/C/D) D
9349((EXPLANATION)) (OPTIONAL)
9350
9351((MARKS)) (1/2/3...)
9352((QUESTION)) The length of Hamiltonian circuit of Kn is__.
9353((OPTION_A)) N
9354((OPTION_B)) n-1
9355((OPTION_C)) n(n - 1) / 2
9356((OPTION_D)) (n - 1)! / 2
9357((CORRECT_CHOICE)) (A/B/C/D) A
9358((EXPLANATION)) (OPTIONAL)
9359
9360((MARKS)) (1/2/3...) 2
9361((QUESTION)) The length of Hamiltonian circuit is__.
9362((OPTION_A)) the number of edges in the circuit
9363((OPTION_B)) the number of vertices in the circuit
9364((OPTION_C)) the number of edges + vertices in the circuit
9365((OPTION_D)) none of these
9366((CORRECT_CHOICE)) (A/B/C/D) b
9367((EXPLANATION)) (OPTIONAL)
9368
9369
9370((MARKS)) (1/2/3...) 2
9371((QUESTION)) A complete graph Kn where n is odd contains__.
9372((OPTION_A)) Eulerian circuit
9373((OPTION_B)) Hamiltonian circuit
9374((OPTION_C)) both (a) and (b)
9375((OPTION_D)) none of these
9376((CORRECT_CHOICE)) (A/B/C/D) c
9377((EXPLANATION)) (OPTIONAL)
9378
9379((MARKS)) (1/2/3...) 2
9380((QUESTION)) If v, e and r are the total number of vertices, edges and regions in the graph, then for any connected planar graph, which condition is satisfied?
9381((OPTION_A)) v + e + r = 2
9382((OPTION_B)) v - e + r = 2
9383((OPTION_C)) v + e - r = 2
9384((OPTION_D)) v - e - r = 2
9385((CORRECT_CHOICE)) (A/B/C/D) b
9386((EXPLANATION)) (OPTIONAL)
9387
9388((MARKS)) (1/2/3...) 2
9389((QUESTION)) which graphs are non planar graphs?
9390((OPTION_A)) K5
9391((OPTION_B)) K3,3
9392((OPTION_C)) both (a) and (b)
9393((OPTION_D)) none of these
9394((CORRECT_CHOICE)) (A/B/C/D) C
9395((EXPLANATION)) (OPTIONAL)
9396
9397((MARKS)) (1/2/3...) 2
9398((QUESTION)) If self loops as well as parallel edges are allowed, the graph is known as ____.
9399((OPTION_A)) multigraph
9400((OPTION_B)) pseudograph
9401((OPTION_C)) simple graph
9402((OPTION_D)) none of these
9403((CORRECT_CHOICE)) (A/B/C/D) b
9404((EXPLANATION)) (OPTIONAL)
9405
9406((MARKS)) (1/2/3...) 2
9407((QUESTION)) If no self loop and no parallel edges are present in a graph, the graph is known as ___
9408((OPTION_A)) multigraph
9409((OPTION_B)) pseudograph
9410((OPTION_C)) simple graph
9411((OPTION_D)) none of these
9412((CORRECT_CHOICE)) (A/B/C/D) C
9413((EXPLANATION)) (OPTIONAL)
9414
9415
9416((MARKS)) (1/2/3...) 2
9417((QUESTION)) If parallel edges are allowed but self loops are not permitted, the graph is known as ___.
9418((OPTION_A)) multigraph
9419((OPTION_B)) pseudograph
9420((OPTION_C)) simple graph
9421((OPTION_D)) none of these
9422((CORRECT_CHOICE)) (A/B/C/D) A
9423((EXPLANATION)) (OPTIONAL)
9424
9425
9426((MARKS)) (1/2/3...)
9427((QUESTION)) How many nodes are necessary to construct a graph with exactly 8 edges in which each node is of degree 2?
9428((OPTION_A)) 2
9429((OPTION_B)) 4
9430((OPTION_C)) 8
9431((OPTION_D)) 16
9432((CORRECT_CHOICE)) (A/B/C/D) C
9433((EXPLANATION)) (OPTIONAL)
9434
9435((MARKS)) (1/2/3...) 2
9436((QUESTION)) The sum of the degrees of the vertices of the graph is___.
9437((OPTION_A)) same as no. of edge
9438((OPTION_B)) twice the no. of edges
9439((OPTION_C)) half the no. of edges
9440((OPTION_D)) none of these
9441((CORRECT_CHOICE)) (A/B/C/D) B
9442((EXPLANATION)) (OPTIONAL)
9443
9444
9445((MARKS)) (1/2/3...) 2
9446((QUESTION)) In a graph the number of vertices of odd degree is ___.
9447((OPTION_A)) Odd
9448((OPTION_B)) Even
9449((OPTION_C)) zero
9450((OPTION_D)) none
9451((CORRECT_CHOICE)) (A/B/C/D) b
9452((EXPLANATION)) (OPTIONAL)
9453
9454((MARKS)) (1/2/3...) 2
9455((QUESTION)) Degree of any vertex of a simple graph with n vertices is at the most__.
9456((OPTION_A)) N
9457((OPTION_B)) N+1
9458((OPTION_C)) n-1
9459((OPTION_D)) 2n
9460((CORRECT_CHOICE)) (A/B/C/D) c
9461((EXPLANATION)) (OPTIONAL)
9462
9463((MARKS)) (1/2/3...) 2
9464((QUESTION)) Maximum number of edges in a simple graph with n vertices is__.
9465((OPTION_A)) n(n+1) / 2
9466((OPTION_B)) n
9467((OPTION_C)) 2n
9468((OPTION_D)) N(n-1)/2
9469((CORRECT_CHOICE)) (A/B/C/D) d
9470((EXPLANATION)) (OPTIONAL)
9471
9472((MARKS)) (1/2/3...) 2
9473((QUESTION)) Determine the number of edges in a graph with 6 nodes, 2 vertices of degree 4 and 4 vertices of degree 2.
9474((OPTION_A)) 4
9475((OPTION_B)) 8
9476((OPTION_C)) 2
9477((OPTION_D)) 16
9478((CORRECT_CHOICE)) (A/B/C/D) b
9479((EXPLANATION)) (OPTIONAL)
9480
9481((MARKS)) (1/2/3...) 2
9482((QUESTION)) An a directed graph, e is an edge from a to b then _____.
9483((OPTION_A)) a is known as initial vertex and b is not a terminal vertex.
9484((OPTION_B)) a is not initial vertex and b is a terminal vertex
9485((OPTION_C)) a is not initial vertex and b is not a terminal vertex.
9486((OPTION_D)) a is initial vertex and b is a terminal vertex.
9487((CORRECT_CHOICE)) (A/B/C/D) D
9488((EXPLANATION)) (OPTIONAL)
9489
9490((MARKS)) (1/2/3...) 2
9491((QUESTION)) A graph with n vertices is a complete graph if ____.
9492((OPTION_A)) degree of each vertex is n
9493((OPTION_B)) degree of each vertex is (n - 1)
9494((OPTION_C)) degree of each vertex is (n + 1)
9495((OPTION_D)) degree of each vertex is 2n
9496((CORRECT_CHOICE)) (A/B/C/D) b
9497((EXPLANATION)) (OPTIONAL)
9498
9499
9500((MARKS)) (1/2/3...) 2
9501((QUESTION)) No. of edges in a complete graph Kn is ____.
9502((OPTION_A)) n
9503((OPTION_B)) n2
9504((OPTION_C)) n(n-1)/2
9505((OPTION_D)) n(n + 1) /2
9506((CORRECT_CHOICE)) (A/B/C/D) C
9507((EXPLANATION)) (OPTIONAL)
9508
9509((MARKS)) (1/2/3...) 1
9510((QUESTION)) Which is true?
9511((OPTION_A)) complete graph <=> regular graph
9512((OPTION_B)) complete graph => regular graph but converse need not be true
9513((OPTION_C)) regular graph => complete graph but converse need not be true
9514((OPTION_D)) none of these
9515((CORRECT_CHOICE)) (A/B/C/D) b
9516((EXPLANATION)) (OPTIONAL)
9517
9518((MARKS)) (1/2/3...) 2
9519((QUESTION)) A complete bipartite graph Km,n is regular if____.
9520((OPTION_A)) m > n
9521((OPTION_B)) m < n
9522((OPTION_C)) m = n
9523((OPTION_D)) none of these
9524((CORRECT_CHOICE)) (A/B/C/D) c
9525((EXPLANATION)) (OPTIONAL)
9526
9527
9528sr. no. Que Option 1 Option 2 Option 3 Option 4 Ans
95291 If self loops as well as parallel edges are allowed, the graph is known as ____. 1) multigraph 2) pseudograph 3) simple graph 4) none of these 2
95302 If no self loop and no parallel edges are present in a graph, the graph is known as ___ . 1) multigraph 2) pseudograph 3) simple graph 4) none of these 3
95313 If parallel edges are allowed but self loops are not permitted, the graph is known as ___. 1) multigraph 2) pseudograph 3) simple graph 4) none of these 1
95324 How many nodes are necessary to construct a graph with exactly 8 edges in which each node is of degree 2? 1) 2 2) 4 3) 8 4) 16 3
95335 The sum of the degrees of the vertices of the graph is___. 1) same as no. of edges 2) twice the no. of edges 3) half the no. of edges 4) none of these 2
95346 In a graph the number of vertices of odd degree is ___. 1) odd 2) even 3) zero 4) none of these 2
95357 Degree of any vertex of a simple graph with n vertices is at the most__. 1) n 2) (n+1) 3) (n-1) 4) 2n 3
95368 Maximum number of edges in a simple graph with n vertices is__. 1) n(n+1) / 2 2) n 3) 2n 4) n(n - 1) / 2 4
95379 Determine the number of edges in a graph with 6 nodes, 2 vertices of degree 4 and 4 vertices of degree 2. 1) 4 2) 8 3) 2 4) 16 2
953810 An a directed graph, e is an edge from a to b then _____. 1) a is known as initial vertex and b is not a terminal vertex. 2) a is not initial vertex and b is a terminal vertex. 3) a is not initial vertex and b is not a terminal vertex. 4) a is initial vertex and b is a terminal vertex. 4
953911 A graph with n vertices is a complete graph if ____. 1) degree of each vertex is n 2) degree of each vertex is (n - 1) 3) degree of each vertex is (n + 1) 4) degree of each vertex is 2n 2
954012 No. of edges in a complete graph Kn is ____. 1) n 2) n2 3) n(n - 1) / 2 4) n(n + 1) /2 3
954113 Which is true? 1) complete graph <=> regular graph 2) complete graph => regular graph but converse need not be true 3) regular graph => complete graph but converse need not be true 4) none of these 2
954214 A complete bipartite graph Km,n is regular if____. 1) m > n 2) m < n 3) m = n 4) none of these 3
954315 How many edges K6 (complete graph with 6 vertices) has? 1) 30 2) 15 3) 6 4) 21 2
954416 How many edges K4,6 has ? 1) 24 2) 10 3) 12 4) 15 1
954517 Which graph is complete bipartite graph but not a regular graph ? 1) K3,3 2) K4,4 3) K1,6 4) none of these 3
954618 If G is graph whosw set of vertices is V. If V can b partitioned into two subsets V1 and V2 such that every edge of G joins V1 with V2 also V1 U V2 =V and V1 1) G is a regular graph 2) G is a bipartite graph 3) G is a complete graph 4) none of these 2
954719 A vertex with degree zero is known as __. 1) Pendant vertex 2) isolated vertex 3) node 4) junction 2
954820 A vertex with degree one is known as __. 1) Pendant vertex 2) isolated vertex 3) node 4) junction 1
954921 How many nodes are necessary to construct a graph with exactly n edges in which each node is of degree 2? 1) n - 1 2) n 3) n + 1 4) 2n 2
955022 A graph is known as null graph if__. 1) it has no edges 2) it has no vertices 3) it has no edges and no vertices 4) none of these 1
955123 A graph with 4 nodes and 7 edges can not be a__. 1) multigraph 2) pseudograph 3) simple graph 4) all of these 3
955224 A subgraph G' of G is known as spanning subgraph if__. 1) G' contains all the edges of G 2) G' contains all the vertices of G 3) both (a) and (b) 4) none of these 2
955325 Two graphs G1 and G2 are isommorphic if__. 1) number of vertices as well as edges in G1 and G2 are same 2) G1 has n vertices of degree k then G2 must have exactly n vertices of degree k 3) adjacency is preserved 4) all of these 4
955426 Under which condition Km,n , the complete bipartite graph will have an Eulerian circuit ? 1) If m = n and both are odd 2) If m != n and either m is odd or n is odd 3) If both m and n are even (m = n or m != n) 4) none of these 3
955527 An undirected graph possesses an Eulerian path if__. 1) it is connected and has either zero or two vertices of odd degree 2) it is connected and has even no. of vertices (> 2) of odd degree 3) both (a) and (b) 4) none of these 1
955628 An undirected graph possesses an Eulerian circuit if__. 1) it is connected and has two vertices of odd degrees 2) it is connected and its vertices are all of even degree 3) both (a) and (b) 4) none of these 2
955729 A graph is known as Eulerian path if __. 1) every vertex of the graph G appears exactly once in the path 2) every edge of the graph G appears exactly once in the path 3) both (a) and (b) 4) none of these 2
955830 A pth in a connected graph G is Hamiltonian path if__. 1) It contains every edge of G exactly once 2) It contains every vertex of G exactly once 3) both (a) and (b) 4) none of these 2
955931 How many Hamiltonian circuits exists in Kn ? 1) n 2) n - 1 3) n(n - 1) / 2 4) (n - 1)! / 2 4
956032 The length of Hamiltonian circuit of Kn is__. 1) n 2) n - 1 3) n(n - 1) / 2 4) (n - 1)! / 2 1
956133 The length of Hamiltonian circuit is__. 1) the number of edges in the circuit 2) the number of vertices in the circuit 3) the number of edges + vertices in the circuit 4) none of these 2
956234 A complete graph Kn where n is odd contains__. 1) Eulerian circuit 2) Hamiltonian circuit 3) both (a) and (b) 4) none of these 3
956335 If v, e and r are the total number of vertices, edges and regions in the graph, then for any connected planar graph, which condition is satisfied? 1) v + e + r = 2 2) v - e + r = 2 3) v + e - r = 2 4) v - e - r = 2 2
956436 which graphs are non planar graphs? 1) K5 2) K3,3 3) both (a) and (b) 4) none of these 3
956537 The length of Hamiltonian Path in a connected graph of n vertices is n–1 n n+1 n/2 1
956638 graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are greater than n–1 less than n(n–1) greater than n(n–1)/2 less than n2/2 1
956739 Length of the walk of a graph is The number of vertices in walk W The number of edges in walk W Total number of edges in a graph Total number of vertices in a graph 2
956840 In an undirected graph the number of nodes with odd degree must be Zero Odd Prime Even 4
956941 An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are all of even degree all of odd degree of any degree even in number 1
957042 Maximum number of edges in a n-Node undirected graph without self loop is n2 n(n – 1) n(n + 1) n(n – 1)/2 4
957143 "Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of
9572distinct cycles of length 4 in G is equal to" 15 30 90 360 1
957344 In any undirected graph the sum of degrees of all the nodes Must be even Are twice the number of edges Must be odd Need not be even 2
957445 If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called... ? K graph K-regular graph Empty graph All of above 2
957546 A connected graph on 15 vertices divides the plane into 12 regions. The number of edges connecting the vertices in this graph will be: 15 23 24 25 4
957647 Indicate which, if any, of the following five graphsG= (V,E,φ),|V|= 5, is not isomorphic to any of the other four. φ=(A{1,3}B{2,4}C{1,2}D{2,3}E{3,5}F{4,5}) φ=(f{1,2}b{1,2}c{2,3}d{3,4}e{3,4}a{4,5}) φ=(b{4,5}f{1,3}e{1,3}d{2,3}c{2,4}a{4,5}) φ=(b{4,5}a{1,3}e{1,3}d{2,3}c{2,5}f{4,5}) 1
957748 Indicate which, if any, of the following five graphsG= (V,E,φ),|V|= 5, is notconnected. φ=(1{1,2}2{1,2}3{2,3}4{3,4}5{1,5}6{1,5}) φ=(b{4,5}a{1,3}e{1,3}d{2,3}c{2,5}f{4,5}) φ=(b{4,5}f{1,3}e{1,3}d{2,3}c{2,4}a{4,5}) φ=(a{1,2}b{2,3}c{1,2}d{1,3}e{2,3}f{4,5}) 4
957849 Indicate which, if any, of the following five graphsG=(V,E,φ),|V|= 5, have an Eulerian circuit. φ=(F{1,2}B{1,2}C{2,3}D{3,4}E{4,5}A{4,5}) φ=(b{4,5}f{1,3}e{1,3}d{2,3}c{2,4}a{4,5}) φ=(1{1,2}2{1,2}3{2,3}4{3,4}5{4,5}6{4,5}) φ=(a{1,3}b{3,4}c{1,2}d{2,3}e{3,5}f{4,5}) 4
957950 A graph withV={1,2,3,4}is described byφ=(a{1,2}b{1,2}c{1,4}d{2,3}e{3,4}f{3,4}).How many Hamiltonian cycles does it have? 1 2 4 16 3
958051 The number of distinct simple graphs with up to three nodes is 15 10 7 9 3
958152 For any graph G, exactly ONE of the following statement is False If the minimum degree of G equals the maximum degree of G, then all vertices of G have the same degree The number of vertices of odd degree is even The number of vertices of even degree is even The sum of the degree of the vertices of G is twice the number of edges of G 3
958253 In connection with "Hamiltonian" property, A tree can possess a Hamiltonian chain under certain conditions Any bipertite graph having an odd number of vertices possesses a Hamiltonian circuit. If a graph possesses a Hamiltonian circuit then it always possesses Hamiltonian chain. Every complete graph has several Hamiltonian circuits. 2
958354 Determine which of the following graph G(V,E) is a simple graph where V={a, b, c, d} and only (iv) (iii) and (iv) (i) and (ii) (ii) and (iv) 1
9584 (i) E=[{a,b},{a,c}, {b,a}, {d,d}, {b,c}, {c,d}, {d,a}]
9585 (ii)E=[{a,b}, {c,d}, {a,b}, {d,b}]
9586 (iii)E=[{a,a}, {b,c}, {d,a}, {d,c}]
9587 (iv)E=[{a,b}, {a,c}, {a,d}, {b,c}, {c,d}]
958855 What is the number of vertices in an undirected connected graph with 27 edges, 6 vertices of degree 2,3 vertices of degree 4 and remaining of degree 3? 10 11 18 19 1
958956 Which of the following graphs has an Euclerian circuit? The complement of a cycle on 25 vertices A complete graph on 90 vertices Any k-regular graph where k is an even number None of these 3
959057 Let G be the non-planer graph with the minimum possible number of edges. Then G has 10 edges and 6 vertices 10 edges and 5 vertices 9 edges and 6 vertices 9 edges and 5 vertices 3
959158 Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is 13 9 8 6 3
959259 Which of the following statements is true for every planar graph on n vertices. The graph has an independent set of size at least n/3 The graph has a vertex-cover of size at most 3n/4 The graph is Eulerian The graph is connected. 2
959360 Which one of the follwing is TRUE for any simple conneted undirected graph with more than 2 vertices? All vertices have the same degree At least three vertices have the same degree At least two vertices have the same degree No two vertices have the same degree 3
9594
9595Sr. No. Question Option 1 Option 2 Option 3 Option 4 Option 5 Option 6 Correct answer(1,2,3,4,5,6) Question type Time(in seconds) Out of marks Explanation
9596
95971 A graph with n vertices will definitely have a parallel edge or self loop of the the total number of edges are_____ more than n more than n+1 more than n+1/2 more than n(n-1)/2 4 Objective 1
95982 Maximum degree of any vertex in simple graph with n vertices is_______ n-1 n+1 n 2n-1 1 Objective 1
95993 A graph is said to be connected if it contain atleast one loop it does not contain cycle it is not simple cannot be partitioned without removing an edge 4 Objective 1
96004 A simple graph with n vertices nd k components can have atmost________ n edges n-k edges (n-k)(n-k-1)/2 edges (n-k)(n-k+1)/2 edges 4 Objective 1
96015 Let G be an undirected graph.Consider a depth-first transversal of G,and let T be the resulting depth-first search tree.Let u be a vertex in G and v be the first new(unvisited) vertex visited after visiting u in the transversal.Which of the following statement is always true? {u,v}must be an edge inG,and u is descendant of v in T {u,v} must be an edge in G,and v is descendant of u in T If {u,v}is not an edge in G,then u is a leaf mode in T If {u,v} is not an edge in G,then u and v must have same parent in T 3 Objective 1
96026 How many undirected graphs can be constructed out of a given set V={v 1,v 2,….v n} of n vertice? n(n-1)/2 2n n! 1n(n-1)/2 4 Objective 1
96037 A circuit in a connected graph which includes every vertex of the graph is called _______ hamiltonian circuict euler circuit clique none of these 1 Objective 1
96048 A graph can be represented as linked list structure union none of these 1 Objective 1
96059 A graph can be represented as array structure union none of these 1 Objective 1
960610 For a simple unidirected graph if there are 10 vertices then at the most ______ number of edges are present 40 20 50 45 4 Objective 1
960711 The most appropriate matching for the following pairs A. Breadth first search 1.Heap B.Depth first search 2.queue C. Complete binary tree 3. Stack A-1 B-2 C-3 A-2 B-3 C-1 A-3 B-2 C-1 A-2 B-1 C-3 2 Objective 1
960812 A subgraph G that contains every vertex of G and is a tree is called trivial tree empty tree binary tree spanning tree 4 Objective 1
960913 Every connected tree________ does not have spanning tree may or may not have spanning tree has a spanning tree none of these 3 Objective 1
961014 A spanning tree of connected graph with 10 vertices contain _______ 9 edges 10 edges 11 edges any number of edges 1 Objective 1
961115 If a graph is a tree then it has ______ 2 spanning trees 1 spanning tree 4 spanning trees no spanning trees 2 Objective 1
961216 which of the following data structure is non linear ? stack Queue Linked list Graph 4 Objective 1
961317 Graph is a collection of……….? rows & columns vertices &edges equations none of the above 2 Objective 1
961418 In graph G if e=[v1,v2] then v1 and v2 are called as… nodes endpoints neighbors alln of these 3 Objective 1
961519 In graph G if e=[v1,v2] then v1 and v2 then that means… v1 & v2 are adjacent to each other v1 & v2 are not connected v2 is source vertex & v1 is sink vertex v1 & v2 are one and the same 1 Objective 1
961620 A graph with no edge is called…. Regular graph bipartite graph trivial graph none of these 3 Objective 1
961721 A graph G is called … if it is connected acyclic graph cyclic graph regular graph tree none of these 3 Objective 1
961822 Which of the following is not a type of graph path graph bipartite graph Hamiltonian Tree 1 Objective 1
961923 The terminal vertices of a path are of degree… 1 2 0 more than 4 1 Objective 1
962024 If every node v1 in G is adjacent to every other node v2 in G then the graph is said to be… Isolated complete finite directed 2 Objective 1
962125 Which data model is used in the network data model? stack linked list tree graph 4 Objective 1
962226 In a graph a vertex with degree 0 is called… Leaf vertex dominating vertex isolated vertex source vertex 3 Objective 1
962327 A vertex with degree n-1 in a graph on n vertices is called a… Leaf vertex dominating vertex isolated vertex source vertex 2 Objective 1
962428 If for some positive integer I, degree of vertex d(u)=I for every vertex u of the graph G, then G is called. empty graph regular graph k-regular graph all of the above 2 Objective 1
962529 In a graph a vertex with degree 1 is called… Leaf vertex dominating vertex isolated vertex source vertex 1 Objective 1
962630 The degree of any vertex of graph is the number of edges incident with vertx the numberof edges in a graph the number of vertices in a graph the number of vertices adjecent to that vertex 1 Objective 1
962731 The complete graph Kn is a regular graph with degree of each vertex n n(n-1) n-2 n-1 4 Objective 1
962832 A simple graph in which there exists an edge between every pair of vertices is called regular graph planner graph eular graph complete graph 4 Objective 1
962933 A simple graph has no loops .What other property must a graph have ? it must be directed it must be undirected it must have at least one vertex it must have multiple edges 4 Objective 1
963034 The no. of colours required to properly colour the vertices of every planer graph is 1 2 3 4 2 Objective 1
963135 If T is a graph having n vertices.T is connected and having exactlyn-1 edges then T is a tree T contains no cycle Addition of new edge will create a cycle Every pair of vertices in T is connected by exactly one path 1 Objective 1
963236 Tree is a Bipartite graph Is a connected raph With n nodes containing n-1 edges All of the abv 4 Objective 1
963337 The minimum number of edges in a connected cyclic graph on n vertices is n-1 n n+1 None 2 Objective 1
963438 The maximum degree of any node in a simple graph with n vertices is_____ n-1 n-2 n/2 n 1 Objective 1
963539 Two isomorphic graphs must have equal number of edges equal number of vertices both a and b none of these 3 Objective 1
963640 A graph is a tree if and only if it is______ connected completely connected minialy connected contain a circuit 3 Objective 1
963741 A given connected graph G is a Eular graph is and oly if all vertices of graph G are of_______ even degree odd degree different degree same degree 1 Objective 1
963842 A complete graph with n vertices is_______Hint:The chromatic number of a graph is the minimum number of colours requird to colour it. 2 chrmtic n-1 chromatic n chromatic n/2 chromatic 3 Objective 1
963943 For a complete graph Kn the n denote the number of_____ edges vertices degree of each vertes none of these 2 Objective 1
964044 Adjacency matrix representation of graph cannot contain information about nodes edges direction of edges parallel edges 4 Objective 1
964145 For undirected graph of n vertices and e edges then sum of degree of each vertex is n(n-1)/2 2e 2n e/2 2 Objective 1
964246 The time complexity of depth first search algorithm which when implemented using adjacency matrix is O(|v|)^2 O(log2|V|) O(|V|) O( |V| + |E| ) 1 Objective 1
964347 The time complexity of depth first search algorithm which when implemented using adjacency list is O(|V|)^2 O(log2|V|) O(|V|) O( |V| + |E| ) 4 Objective 1
964448 The time complexity of breadth first search algorithm which when implemented using adjamcy matrix is O(|V|)^2 O(log2|V|) O(|V|) O( |V| + |E| ) 1 Objective 1
964549 The time complexity of breadthth first search algorithm which when implemented using adjacency list is O(|v|)^2 O(log^2|V|) O(|V|) O( |V| + |E| ) 4 Objective 1
964650 Breadth first traversal is a method of a single path of a graph as long as it goes graph using shortest path all successors of a visited node before any successors of any of those successors none of these 3 Objective 1
964751 Transitive closure is obtained using stack queue tree graph 4 Objective 1
964852 A vertex of a graph is called even or odd depending upon total number of edges in the graph are even or odd its degree is even or odd total number of vertices in the graph are even or odd none of these 2 Objective 1
964953 Which of the following statements is/are TRUE for an undirected graph p: Number of odd degree vertices is even q: sum of degree of all vertices is even P only Q only P&Q only Neither P Nor Q 3 Objective 1
965054 Application of graph are game playing circuit planning GIS All of these 4 Objective 1
965155 A null graph containing the 4 vertices in which the degree of each vertex is zero two three four 1 Objective 1
965256 A star graph is_________ regular graph cyclic graph isomorphic complete bipartite graph 4 Objective 1
965357 The maximum degree of any vertx in any graph of 3 vertices is______ 4 1 2 3 3 Objective 1
965458 A simple graph has 15 edges and 3 vertices of degree 4 of all other vertices of degree 3 how many vertices does the graph have 8 9 10 11 2 Objective 1
965559 The degree of any vertex of graph is The number of edges incident with vertex The number of edges in a graph The number vertices in a graph The number of vertices adjacent to the vertex 1 Objective 1
965660 The number of loops in a simple graph are One n n-1 Zero 4 Objective 1
965761 Length of a walk of agraph denotes Total no. of vertices in a walk Total no. of edges in awalk shortest distance in a graph None of these 2 Objective 1
965862 If the origin and termination of the walk is the same then the walk is kniwn as open close path distance 2 Objective 1
965963 Which of the following data stucture is used by breadth first search as an auxiliary sructure to holds nodes for future processing? Queue Stack Tree Graph 1 Objective 1
966064 Which of the following data stucture is used by depth first search as an auxiliary sructure to holds nodes for future processing? Queue Stack Tree Graph 2 Objective 1
966165 Which of the data sructure is used in implementing a graph using adjacency matrix? arrays Linked list stack Queue 1 Objective 1
966266 Which of the data sructure is used in implementing a graph using adjacency list? Arrays Linked list stack Queue 2 Objective 1
966367 In adjacency matrix representation of graph if M[u][v]=0 then it indicates There exists an edge from u to v but not from v to u There exists an edge from v to u but not from u to v There no direct edge present between u and v None of these 3 Objective 1
966468 Graph can be represented using adjacency tree adjacency linked list adjacency graph none of these 2 Objective 1
966569 A complete with n nodes will have n edges n-1 edges n(n+1)edges n(n-1)/2 edges 4 Objective 1
966670 Adjacency matrix of digraph is sparse matrix symmetric matrix asymmetric matrix identity matrix 3 Objective 1
966771 If a graph G has no edge then the corrosponding adjacency matrix is called unit matrix zero matrix sparse matrix none of these 2 Objective 1
966872 For an adjacency matrix of a graph G which does not contain any self loop the entries along the principle diagonal are all ones all zeros both zeros and ones none of these 2 Objective 1
966973 The number of distinct simple graphs with upto three nodes is 15 10 7 9 3 Objective 1
967074 In any undirected graph the sum of degrees of all nodes must be odd must be even not necessarily even is twice the number of edges 4 Objective 1
9671
9672
9673
9674
9675((MARKS)) (1/2/3...) 2
9676((QUESTION)) A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are_____
9677((OPTION_A)) more than n
9678((OPTION_B)) more than n+1
9679((OPTION_C)) more than n+1/2
9680((OPTION_D)) more than n(n-1)/2
9681((CORRECT_CHOICE)) (A/B/C/D) D
9682((EXPLANATION)) (OPTIONAL)
9683
9684
9685((MARKS)) (1/2/3...) 2
9686((QUESTION)) Maximum degree of any vertex in simple graph with n vertices is_______
9687((OPTION_A)) n-1
9688((OPTION_B)) n+1
9689((OPTION_C)) n
9690((OPTION_D)) None
9691((CORRECT_CHOICE)) (A/B/C/D) A
9692((EXPLANATION)) (OPTIONAL)
9693
9694((MARKS)) (1/2/3...) 1
9695((QUESTION)) A graph is said to be connected if
9696((OPTION_A)) it contain atleast one loop
9697((OPTION_B)) it does not contain cycle
9698((OPTION_C)) it is not simple
9699((OPTION_D)) cannot be partitioned without removing an edge
9700((CORRECT_CHOICE)) (A/B/C/D) D
9701((EXPLANATION)) (OPTIONAL)
9702
9703
9704((MARKS)) (1/2/3...) 1
9705((QUESTION)) A simple graph with n vertices and k components can have atmost________
9706((OPTION_A)) n edges
9707((OPTION_B)) n-k edges
9708((OPTION_C)) (n-k)(n-k-1)/2 edges
9709((OPTION_D)) (n-k)(n-k+1)/2 edges
9710((CORRECT_CHOICE)) (A/B/C/D) D
9711((EXPLANATION)) (OPTIONAL)
9712
9713((MARKS)) (1/2/3...) 1
9714((QUESTION)) How many undirected graphs can be constructed out of a given set V={v 1,v 2,….v n} of n vertice?
9715
9716((OPTION_A)) n(n-1)/2
9717((OPTION_B)) 2n
9718((OPTION_C)) n!
9719((OPTION_D)) 1n(n-1)/2
9720
9721((CORRECT_CHOICE)) (A/B/C/D) D
9722((EXPLANATION)) (OPTIONAL)
9723
9724
9725((MARKS)) (1/2/3...) 1
9726((QUESTION)) A circuit in a connected graph which includes every vertex of the graph is called
9727((OPTION_A)) hamiltonian circuict
9728((OPTION_B)) euler circuit
9729((OPTION_C)) Clique
9730((OPTION_D)) none of these
9731((CORRECT_CHOICE)) (A/B/C/D) A
9732((EXPLANATION)) (OPTIONAL)
9733
9734((MARKS)) (1/2/3...) 1
9735((QUESTION)) A graph can be represented as
9736((OPTION_A)) linked list
9737
9738((OPTION_B)) Structure
9739((OPTION_C)) Union
9740((OPTION_D)) none of these
9741((CORRECT_CHOICE)) (A/B/C/D) A
9742((EXPLANATION)) (OPTIONAL)
9743
9744
9745((MARKS)) (1/2/3...) 1
9746((QUESTION)) For a simple unidirected graph if there are 10 vertices then at the most ______ number of edges are present
9747((OPTION_A)) 40
9748((OPTION_B)) 20
9749((OPTION_C)) 50
9750((OPTION_D)) 45
9751((CORRECT_CHOICE)) (A/B/C/D) D
9752((EXPLANATION)) (OPTIONAL)
9753
9754((MARKS)) (1/2/3...) 1
9755((QUESTION)) Graph is a collection of……….?
9756((OPTION_A)) rows & columns
9757((OPTION_B)) vertices &edges
9758((OPTION_C)) Equations
9759((OPTION_D)) none of the above
9760((CORRECT_CHOICE)) (A/B/C/D) B
9761((EXPLANATION)) (OPTIONAL)
9762
9763
9764((MARKS)) (1/2/3...) 1
9765((QUESTION)) A graph with no edge is called….
9766((OPTION_A)) Regular graph
9767((OPTION_B)) bipartite graph
9768((OPTION_C)) trivial graph
9769((OPTION_D)) none of these
9770((CORRECT_CHOICE)) (A/B/C/D) C
9771((EXPLANATION)) (OPTIONAL)
9772
9773((MARKS)) (1/2/3...) 1
9774((QUESTION)) Which of the following is not a type of graph
9775((OPTION_A)) path graph
9776((OPTION_B)) bipartite graph
9777
9778((OPTION_C)) Hamiltonian
9779
9780((OPTION_D)) Tree
9781
9782((CORRECT_CHOICE)) (A/B/C/D) A
9783((EXPLANATION)) (OPTIONAL)
9784
9785
9786((MARKS)) (1/2/3...) 1
9787((QUESTION)) If every node v1 in G is adjacent to every other node v2 in G then the graph is said to be…
9788
9789((OPTION_A)) Isolated
9790
9791((OPTION_B)) complete
9792
9793((OPTION_C)) finite
9794
9795((OPTION_D)) directed
9796
9797((CORRECT_CHOICE)) (A/B/C/D) B
9798((EXPLANATION)) (OPTIONAL)
9799
9800((MARKS)) (1/2/3...) 1
9801((QUESTION)) Which data model is used in the network data model?
9802
9803((OPTION_A)) stack
9804
9805((OPTION_B)) linked list
9806
9807((OPTION_C)) tree
9808
9809((OPTION_D)) graph
9810
9811((CORRECT_CHOICE)) (A/B/C/D) D
9812((EXPLANATION)) (OPTIONAL)
9813
9814
9815((MARKS)) (1/2/3...) 1
9816((QUESTION)) In a graph a vertex with degree 0 is called…
9817
9818((OPTION_A)) Leaf vertex
9819
9820((OPTION_B)) dominating vertex
9821
9822((OPTION_C)) isolated vertex
9823
9824((OPTION_D)) source vertex
9825
9826((CORRECT_CHOICE)) (A/B/C/D) C
9827((EXPLANATION)) (OPTIONAL)
9828
9829((MARKS)) (1/2/3...) 1
9830((QUESTION)) If for some positive integer I, degree of vertex d(u)=I for every vertex u of the graph G, then G is called.
9831
9832((OPTION_A)) empty graph
9833
9834((OPTION_B)) regular graph
9835
9836((OPTION_C)) k-regular graph
9837
9838((OPTION_D)) all of the above
9839
9840((CORRECT_CHOICE)) (A/B/C/D) B
9841((EXPLANATION)) (OPTIONAL)
9842
9843
9844((MARKS)) (1/2/3...) 1
9845((QUESTION)) The complete graph Kn is a regular graph with degree of each vertex
9846
9847((OPTION_A)) n
9848
9849((OPTION_B)) n-1
9850((OPTION_C)) N+1
9851((OPTION_D)) None
9852((CORRECT_CHOICE)) (A/B/C/D) B
9853((EXPLANATION)) (OPTIONAL)
9854
9855((MARKS)) (1/2/3...) 1
9856((QUESTION)) The number of distinct simple graphs with upto three nodes is
9857
9858((OPTION_A)) 15
9859((OPTION_B)) 10
9860((OPTION_C)) 7
9861((OPTION_D)) 9
9862((CORRECT_CHOICE)) (A/B/C/D) C
9863((EXPLANATION)) (OPTIONAL)
9864
9865
9866((MARKS)) (1/2/3...) 1
9867((QUESTION)) In any undirected graph the sum of degrees of all nodes
9868
9869((OPTION_A)) must be odd
9870
9871((OPTION_B)) must be even
9872
9873((OPTION_C)) not necessarily even
9874
9875((OPTION_D)) is twice the number of edges
9876
9877((CORRECT_CHOICE)) (A/B/C/D) D
9878((EXPLANATION)) (OPTIONAL)
9879
9880((MARKS)) (1/2/3...) 2
9881((QUESTION)) If a graph G has no edge then the corrosponding adjacency matrix is called
9882
9883((OPTION_A)) unit matrix
9884
9885((OPTION_B)) zero matrix
9886
9887((OPTION_C)) sparse matrix
9888((OPTION_D)) None
9889((CORRECT_CHOICE)) (A/B/C/D) B
9890((EXPLANATION)) (OPTIONAL)
9891
9892
9893((MARKS)) (1/2/3...) 2
9894((QUESTION)) In adjacency matrix representation of graph if M[u][v]=0 then it indicates
9895
9896((OPTION_A)) There exists an edge from u to v but not from v to u
9897
9898((OPTION_B)) There exists an edge from v to u but not from u to v
9899
9900((OPTION_C)) There no direct edge present between u and v
9901
9902((OPTION_D)) None of these
9903
9904((CORRECT_CHOICE)) (A/B/C/D) C
9905((EXPLANATION)) (OPTIONAL)
9906
9907((MARKS)) (1/2/3...) 2
9908((QUESTION)) The number of loops in a simple graph are
9909
9910((OPTION_A)) 1
9911((OPTION_B)) N
9912((OPTION_C)) n-1
9913((OPTION_D)) 0
9914((CORRECT_CHOICE)) (A/B/C/D) D
9915((EXPLANATION)) (OPTIONAL)
9916
9917
9918((MARKS)) (1/2/3...) 2
9919((QUESTION)) A simple graph has 15 edges and 3 vertices of degree 4 of all other vertices of degree 3 how many vertices does the graph have
9920
9921((OPTION_A)) 8
9922((OPTION_B)) 9
9923((OPTION_C)) 10
9924((OPTION_D)) 11
9925((CORRECT_CHOICE)) (A/B/C/D) B
9926((EXPLANATION)) (OPTIONAL)
9927
9928((MARKS)) (1/2/3...) 2
9929((QUESTION)) A star graph is_________
9930
9931((OPTION_A)) regular graph
9932
9933((OPTION_B)) cyclic graph
9934
9935((OPTION_C)) isomorphic
9936
9937((OPTION_D)) complete bipartite graph
9938
9939((CORRECT_CHOICE)) (A/B/C/D) D
9940((EXPLANATION)) (OPTIONAL)
9941
9942
9943((MARKS)) (1/2/3...) 2
9944((QUESTION)) A null graph containing the 4 vertices in which the degree of each vertex is
9945
9946((OPTION_A)) 2
9947((OPTION_B)) 0
9948((OPTION_C)) 3
9949((OPTION_D)) 4
9950((CORRECT_CHOICE)) (A/B/C/D) B
9951((EXPLANATION)) (OPTIONAL)
9952
9953((MARKS)) (1/2/3...) 2
9954((QUESTION)) Application of graph are
9955
9956((OPTION_A)) game playing
9957
9958((OPTION_B)) circuit planning
9959
9960((OPTION_C)) GIS
9961
9962((OPTION_D)) All of these
9963
9964((CORRECT_CHOICE)) (A/B/C/D) D
9965((EXPLANATION)) (OPTIONAL)
9966
9967((MARKS)) (1/2/3...) 2
9968((QUESTION)) Which of the following statements is/are TRUE for an undirected graph p: Number of odd degree vertices is even q: sum of degree of all vertices is even
9969
9970((OPTION_A)) P only
9971
9972((OPTION_B)) Q only
9973
9974((OPTION_C)) P&Q only
9975
9976((OPTION_D)) Neither P Nor Q
9977
9978((CORRECT_CHOICE)) (A/B/C/D) C
9979((EXPLANATION)) (OPTIONAL)
9980
9981
9982((MARKS)) (1/2/3...) 2
9983((QUESTION)) Adjacency matrix representation of graph cannot contain information about
9984
9985((OPTION_A)) Nodes
9986
9987((OPTION_B)) Edges
9988
9989((OPTION_C)) direction of edges
9990
9991((OPTION_D)) parallel edges
9992
9993((CORRECT_CHOICE)) (A/B/C/D) D
9994((EXPLANATION)) (OPTIONAL)
9995
9996((MARKS)) (1/2/3...) 2
9997((QUESTION)) Subgroup of ( Z8 , + ) generated by [2] is
9998((OPTION_A)) {[0] , [2]}
9999((OPTION_B)) {[0],[1],[3]}
10000((OPTION_C)) {[0],[2],[4],[6]}
10001((OPTION_D)) None
10002((CORRECT_CHOICE)) (A/B/C/D) C
10003((EXPLANATION)) (OPTIONAL)
10004
10005
10006((MARKS)) (1/2/3...) 1
10007((QUESTION))
10008((OPTION_A))
10009((OPTION_B))
10010((OPTION_C))
10011((OPTION_D))
10012((CORRECT_CHOICE)) (A/B/C/D)
10013
10014
10015((MARKS)) (1/2/3...) 1
10016((QUESTION)) In the following graph Adjacent edges are
10017
10018
10019
10020
10021
10022
10023
10024((OPTION_A)) e1, e3
10025((OPTION_B)) e2,e5
10026((OPTION_C)) e1,e4
10027((OPTION_D)) None of these
10028((CORRECT_CHOICE)) (A/B/C/D) B
10029((EXPLANATION)) (OPTIONAL)
10030
10031
10032
10033((MARKS)) (1/2/3...) 1
10034((QUESTION)) The pendent vertices are the vertices
10035((OPTION_A)) Whose degree is two
10036((OPTION_B)) Who are adjacent to any two vertices in the graph
10037((OPTION_C)) Whose degree is one
10038((OPTION_D)) None of these
10039((CORRECT_CHOICE)) (A/B/C/D) C
10040((EXPLANATION)) (OPTIONAL)
10041
10042((MARKS)) (1/2/3...) 1
10043((QUESTION)) A vertex of degree zero in the graph is
10044((OPTION_A)) Pendant vertex
10045((OPTION_B)) Isolated Vertex
10046((OPTION_C)) Adjacent Vertex
10047((OPTION_D)) None of these
10048((CORRECT_CHOICE)) (A/B/C/D) B
10049
10050((MARKS)) (1/2/3...) 1
10051((QUESTION)) A graph without selfloop and without parallel edges are
10052((OPTION_A)) Planner
10053((OPTION_B)) Weighted
10054((OPTION_C)) Simple
10055((OPTION_D)) Multiple
10056((CORRECT_CHOICE)) (A/B/C/D) C
10057
10058
10059
10060
10061((MARKS)) (1/2/3...) 1
10062((QUESTION)) Maximum degree of any vertex in a simple graph with n vertices is
10063((OPTION_A)) n!
10064((OPTION_B)) n+1
10065((OPTION_C)) n-1
10066((OPTION_D)) N
10067((CORRECT_CHOICE)) (A/B/C/D) C
10068
10069((MARKS)) (1/2/3...) 1
10070((QUESTION)) The number of edges in a graph with 6 nodes in which 2 nodes are of egree 4 and remaining nodes are of degree 2 is
10071((OPTION_A)) 7
10072((OPTION_B)) 8
10073((OPTION_C)) 6
10074((OPTION_D)) 5
10075((CORRECT_CHOICE)) (A/B/C/D) B
10076((EXPLANATION)) (OPTIONAL)
10077
10078((MARKS)) (1/2/3...) 1
10079((QUESTION)) The number of nodes required to construct a graph with exactly 6 edges each node is of degree 2 is
10080((OPTION_A)) 5
10081((OPTION_B)) 8
10082((OPTION_C)) 6
10083((OPTION_D)) 4
10084((CORRECT_CHOICE)) (A/B/C/D) C
10085((EXPLANATION)) (OPTIONAL)
10086
10087((MARKS)) (1/2/3...) 1
10088((QUESTION)) The number of nodes required to construct a graph with exactly 8 edges each node is of degree 2 is
10089((OPTION_A)) 8
10090((OPTION_B)) 7
10091((OPTION_C)) 6
10092((OPTION_D)) 5
10093((CORRECT_CHOICE)) (A/B/C/D) A
10094((EXPLANATION)) (OPTIONAL)
10095
10096((MARKS)) (1/2/3...) 1
10097((QUESTION)) If G is a simple graph on n vertices and degree
10098 of each vertex is n-1 then graph is
10099
10100((OPTION_A)) Bipartite
10101((OPTION_B)) Regular
10102((OPTION_C)) Null
10103((OPTION_D)) Complete
10104((CORRECT_CHOICE)) (A/B/C/D) C
10105((EXPLANATION)) (OPTIONAL)
10106
10107((MARKS)) (1/2/3...) 1
10108((QUESTION)) A degree of each vertex is same in the graph hen
10109 the graph is
10110((OPTION_A)) Bipartite
10111((OPTION_B)) Regular
10112((OPTION_C)) Complete Bipartite
10113((OPTION_D)) Complete
10114((CORRECT_CHOICE)) (A/B/C/D)
10115B
10116((EXPLANATION)) (OPTIONAL)
10117
10118((MARKS)) (1/2/3...) 1
10119((QUESTION)) The complete graph on 3 vertices is also a
10120((OPTION_A)) Regular graph
10121((OPTION_B)) Null Graph
10122((OPTION_C)) Bipartite Graph
10123((OPTION_D)) None of these
10124((CORRECT_CHOICE)) (A/B/C/D) A
10125((EXPLANATION)) (OPTIONAL)
10126
10127((MARKS)) (1/2/3...) 1
10128((QUESTION)) Every complete Graph is
10129((OPTION_A)) Bipartite
10130((OPTION_B)) Regular
10131((OPTION_C)) Simple
10132((OPTION_D)) None of these
10133((CORRECT_CHOICE)) (A/B/C/D) B
10134((EXPLANATION)) (OPTIONAL)
10135
10136((MARKS)) (1/2/3...) 1
10137((QUESTION)) The number of edges in a complete graph K5 has
10138((OPTION_A)) 5
10139((OPTION_B)) 6
10140((OPTION_C)) 9
10141((OPTION_D)) 10
10142((CORRECT_CHOICE)) (A/B/C/D) D
10143((EXPLANATION)) (OPTIONAL)
10144
10145((MARKS)) (1/2/3...) 1
10146((QUESTION)) The number of edges in complete bipartite graph K3,4 has
10147((OPTION_A)) 10
10148((OPTION_B)) 9
10149((OPTION_C)) 8
10150((OPTION_D)) 12
10151((CORRECT_CHOICE)) (A/B/C/D) D
10152((EXPLANATION)) (OPTIONAL)
10153
10154((MARKS)) (1/2/3...) 1
10155((QUESTION)) H is a spanning sub graph of G such that degree of each vertex in H is k then H is called
10156((OPTION_A)) K-factor graph of G
10157((OPTION_B)) Null sub graph of G
10158((OPTION_C)) Complement of Graph G
10159((OPTION_D)) None of these
10160((CORRECT_CHOICE)) (A/B/C/D) A
10161((EXPLANATION)) (OPTIONAL)
10162
10163((MARKS)) (1/2/3...) 1
10164((QUESTION)) A graph G is Isomorphic to its complement then G is called
10165((OPTION_A)) Complete Graph
10166((OPTION_B)) Bipartite Graph
10167((OPTION_C)) Self complementary Graph
10168((OPTION_D)) None of these
10169((CORRECT_CHOICE)) (A/B/C/D) C
10170((EXPLANATION)) (OPTIONAL)
10171
10172((MARKS)) (1/2/3...) 1
10173((QUESTION)) The edge connectivity of for a complete Graph K6 on six vertices is
10174((OPTION_A)) 3
10175((OPTION_B)) 5
10176((OPTION_C)) 4
10177((OPTION_D)) 2
10178((CORRECT_CHOICE)) (A/B/C/D) B
10179((EXPLANATION)) (OPTIONAL)
10180
10181((MARKS)) (1/2/3...) 1
10182((QUESTION)) The vertex connectivity for the complete bipartite graph K3,4 is
10183((OPTION_A)) 2
10184((OPTION_B)) 1
10185((OPTION_C)) 3
10186((OPTION_D)) 4
10187((CORRECT_CHOICE)) (A/B/C/D) C
10188((EXPLANATION)) (OPTIONAL)
10189
10190
10191
10192((MARKS)) (1/2/3...) 1
10193((QUESTION)) A path in which every edge of the graph appers exactly once is
10194((OPTION_A)) Hamiltonian
10195((OPTION_B)) Eulerian
10196((OPTION_C)) Hamiltonian Circuit
10197((OPTION_D)) None of these
10198((CORRECT_CHOICE)) (A/B/C/D) B
10199((EXPLANATION)) (OPTIONAL)
10200
10201((MARKS)) (1/2/3...) 1
10202((QUESTION)) A circuit which contains every edge of the graph exactly once is
10203((OPTION_A)) Eulerian circuit
10204((OPTION_B)) Hamiltonian circuit
10205((OPTION_C)) Hamiltonian graph
10206((OPTION_D)) None of these
10207((CORRECT_CHOICE)) (A/B/C/D) A
10208((EXPLANATION)) (OPTIONAL)
10209
10210((MARKS)) (1/2/3...) 1
10211((QUESTION)) A graph which has an Eulerian circuit is
10212((OPTION_A)) Hamiltonian graph
10213((OPTION_B)) Complete bipartite graph
10214((OPTION_C)) Eulerian graph
10215((OPTION_D)) None of these
10216((CORRECT_CHOICE)) (A/B/C/D) C
10217((EXPLANATION)) (OPTIONAL)
10218
10219((MARKS)) (1/2/3...) 1
10220((QUESTION)) A graph possesses an Eulerian circuit if and only if it is connected and has vertices which all have
10221((OPTION_A)) Even degree
10222((OPTION_B)) Odd degree
10223((OPTION_C)) Degree one
10224((OPTION_D)) Degree three
10225((CORRECT_CHOICE)) (A/B/C/D) A
10226((EXPLANATION)) (OPTIONAL)
10227
10228((MARKS)) (1/2/3...) 1
10229((QUESTION)) A path in which every vertex of the graph appears exactly once is
10230((OPTION_A)) Eulerian path
10231((OPTION_B)) Hamiltonian path
10232((OPTION_C)) Eulerian circuit
10233((OPTION_D)) Hamiltonian circuit
10234((CORRECT_CHOICE)) (A/B/C/D) B
10235((EXPLANATION)) (OPTIONAL)
10236
10237((MARKS)) (1/2/3...) 1
10238((QUESTION)) A graph which has Hamiltonian circuit is called
10239((OPTION_A)) Hamiltonian graph
10240((OPTION_B)) Complete bipartite graph
10241((OPTION_C)) Eulerian graph
10242((OPTION_D)) None of these
10243((CORRECT_CHOICE)) (A/B/C/D) A
10244((EXPLANATION)) (OPTIONAL)
10245
10246((MARKS)) (1/2/3...) 1
10247((QUESTION)) A complete graph k4 on four vertices has
10248((OPTION_A)) Eulerian circuit
10249((OPTION_B)) Hamiltonian circuit
10250((OPTION_C)) Neither Eulerian nor Hamiltonian circuit
10251((OPTION_D)) Both Eulerian and Hamiltonian circuit
10252((CORRECT_CHOICE)) (A/B/C/D) D
10253((EXPLANATION)) (OPTIONAL)
10254
10255((MARKS)) (1/2/3...) 2
10256((QUESTION)) How many edges must a planar graph have if it has 7 regions and 5 vertices?
10257((OPTION_A)) 9
10258((OPTION_B)) 10
10259((OPTION_C)) 8
10260((OPTION_D)) 7
10261((CORRECT_CHOICE)) (A/B/C/D) B
10262((EXPLANATION)) (OPTIONAL)
10263
10264((MARKS)) (1/2/3...) 2
10265((QUESTION)) The number of regions defined by a connected planar graph with 6 vertices and 10 edges are
10266((OPTION_A)) 6
10267((OPTION_B)) 7
10268((OPTION_C)) 5
10269((OPTION_D)) 4
10270((CORRECT_CHOICE)) (A/B/C/D) A
10271((EXPLANATION)) (OPTIONAL)
10272
10273((MARKS)) (1/2/3...) 2
10274((QUESTION)) A connected planar graph has nine vertices having 2,2,2,3,3,3,4,4 and 5. The number of regions it has is
10275((OPTION_A)) 6
10276((OPTION_B)) 5
10277((OPTION_C)) 7
10278((OPTION_D)) 9
10279((CORRECT_CHOICE)) (A/B/C/D) C
10280((EXPLANATION)) (OPTIONAL)
10281
10282((MARKS)) (1/2/3...) 1
10283((QUESTION)) The following graph is
10284
10285
10286
10287
10288
10289
10290((OPTION_A)) Planar graph
10291((OPTION_B)) Complete graph
10292((OPTION_C)) Regular graph
10293((OPTION_D)) None of these
10294((CORRECT_CHOICE)) (A/B/C/D) A
10295((EXPLANATION)) (OPTIONAL)
10296
10297((MARKS)) (1/2/3...) 1
10298((QUESTION)) A graph which can be drawn on the plane such that no edges cross each other called
10299((OPTION_A)) Complete
10300((OPTION_B)) Regular
10301((OPTION_C)) Planar
10302((OPTION_D)) Complete bipartite graph
10303((CORRECT_CHOICE)) (A/B/C/D) C
10304((EXPLANATION)) (OPTIONAL)
10305
10306
10307((MARKS)) (1/2/3...) 1
10308((QUESTION)) In the following graph parallel edges are
10309
10310
10311
10312
10313
10314((OPTION_A)) e1, e2
10315((OPTION_B)) e2, e3
10316((OPTION_C)) e3, e5
10317((OPTION_D)) e3 , e4
10318((CORRECT_CHOICE)) (A/B/C/D) D
10319
10320
10321((MARKS)) (1/2/3...) 1
10322((QUESTION)) In the following graph Adjacent edges are
10323
10324
10325
10326
10327
10328
10329
10330((OPTION_A)) e1, e3
10331((OPTION_B)) e2,e5
10332((OPTION_C)) e1,e4
10333((OPTION_D)) None of these
10334((CORRECT_CHOICE)) (A/B/C/D) B
10335((EXPLANATION)) (OPTIONAL)
10336
10337
10338
10339((MARKS)) (1/2/3...) 1
10340((QUESTION)) The pendent vertices are the vertices
10341((OPTION_A)) Whose degree is two
10342((OPTION_B)) Who are adjacent to any two vertices in the graph
10343((OPTION_C)) Whose degree is one
10344((OPTION_D)) None of these
10345((CORRECT_CHOICE)) (A/B/C/D) C
10346((EXPLANATION)) (OPTIONAL)
10347
10348((MARKS)) (1/2/3...) 1
10349((QUESTION)) A vertex of degree zero in the graph is
10350((OPTION_A)) Pendant vertex
10351((OPTION_B)) Isolated Vertex
10352((OPTION_C)) Adjacent Vertex
10353((OPTION_D)) None of these
10354((CORRECT_CHOICE)) (A/B/C/D) B
10355
10356((MARKS)) (1/2/3...) 1
10357((QUESTION)) A graph without selfloop and without parallel edges are
10358((OPTION_A)) Planner
10359((OPTION_B)) Weighted
10360((OPTION_C)) Simple
10361((OPTION_D)) Multiple
10362((CORRECT_CHOICE)) (A/B/C/D) C
10363
10364
10365
10366
10367((MARKS)) (1/2/3...) 1
10368((QUESTION)) Maximum degree of any vertex in a simple graph with n vertices is
10369((OPTION_A)) n!
10370((OPTION_B)) n+1
10371((OPTION_C)) n-1
10372((OPTION_D)) N
10373((CORRECT_CHOICE)) (A/B/C/D) C
10374
10375((MARKS)) (1/2/3...) 1
10376((QUESTION)) The number of edges in a graph with 6 nodes in which 2 nodes are of egree 4 and remaining nodes are of degree 2 is
10377((OPTION_A)) 7
10378((OPTION_B)) 8
10379((OPTION_C)) 6
10380((OPTION_D)) 5
10381((CORRECT_CHOICE)) (A/B/C/D) B
10382((EXPLANATION)) (OPTIONAL)
10383
10384((MARKS)) (1/2/3...) 1
10385((QUESTION)) The number of nodes required to construct a graph with exactly 6 edges each node is of degree 2 is
10386((OPTION_A)) 5
10387((OPTION_B)) 8
10388((OPTION_C)) 6
10389((OPTION_D)) 4
10390((CORRECT_CHOICE)) (A/B/C/D) C
10391((EXPLANATION)) (OPTIONAL)
10392
10393((MARKS)) (1/2/3...) 1
10394((QUESTION)) The number of nodes required to construct a graph with exactly 8 edges each node is of degree 2 is
10395((OPTION_A)) 8
10396((OPTION_B)) 7
10397((OPTION_C)) 6
10398((OPTION_D)) 5
10399((CORRECT_CHOICE)) (A/B/C/D) A
10400((EXPLANATION)) (OPTIONAL)
10401
10402((MARKS)) (1/2/3...) 1
10403((QUESTION)) If G is a simple graph on n vertices and degree
10404 of each vertex is n-1 then graph is
10405
10406((OPTION_A)) Bipartite
10407((OPTION_B)) Regular
10408((OPTION_C)) Null
10409((OPTION_D)) Complete
10410((CORRECT_CHOICE)) (A/B/C/D) C
10411((EXPLANATION)) (OPTIONAL)
10412
10413((MARKS)) (1/2/3...) 1
10414((QUESTION)) A degree of each vertex is same in the graph hen
10415 the graph is
10416((OPTION_A)) Bipartite
10417((OPTION_B)) Regular
10418((OPTION_C)) Complete Bipartite
10419((OPTION_D)) Complete
10420((CORRECT_CHOICE)) (A/B/C/D)
10421B
10422((EXPLANATION)) (OPTIONAL)
10423
10424((MARKS)) (1/2/3...) 1
10425((QUESTION)) The complete graph on 3 vertices is also a
10426((OPTION_A)) Regular graph
10427((OPTION_B)) Null Graph
10428((OPTION_C)) Bipartite Graph
10429((OPTION_D)) None of these
10430((CORRECT_CHOICE)) (A/B/C/D) A
10431((EXPLANATION)) (OPTIONAL)
10432
10433((MARKS)) (1/2/3...) 1
10434((QUESTION)) Every complete Graph is
10435((OPTION_A)) Bipartite
10436((OPTION_B)) Regular
10437((OPTION_C)) Simple
10438((OPTION_D)) None of these
10439((CORRECT_CHOICE)) (A/B/C/D) B
10440((EXPLANATION)) (OPTIONAL)
10441
10442((MARKS)) (1/2/3...) 1
10443((QUESTION)) The number of edges in a complete graph K5 has
10444((OPTION_A)) 5
10445((OPTION_B)) 6
10446((OPTION_C)) 9
10447((OPTION_D)) 10
10448((CORRECT_CHOICE)) (A/B/C/D) D
10449((EXPLANATION)) (OPTIONAL)
10450
10451((MARKS)) (1/2/3...) 1
10452((QUESTION)) The number of edges in complete bipartite graph K3,4 has
10453((OPTION_A)) 10
10454((OPTION_B)) 9
10455((OPTION_C)) 8
10456((OPTION_D)) 12
10457((CORRECT_CHOICE)) (A/B/C/D) D
10458((EXPLANATION)) (OPTIONAL)
10459
10460((MARKS)) (1/2/3...) 1
10461((QUESTION)) H is a spanning sub graph of G such that degree of each vertex in H is k then H is called
10462((OPTION_A)) K-factor graph of G
10463((OPTION_B)) Null sub graph of G
10464((OPTION_C)) Complement of Graph G
10465((OPTION_D)) None of these
10466((CORRECT_CHOICE)) (A/B/C/D) A
10467((EXPLANATION)) (OPTIONAL)
10468
10469((MARKS)) (1/2/3...) 1
10470((QUESTION)) A graph G is Isomorphic to its complement then G is called
10471((OPTION_A)) Complete Graph
10472((OPTION_B)) Bipartite Graph
10473((OPTION_C)) Self complementary Graph
10474((OPTION_D)) None of these
10475((CORRECT_CHOICE)) (A/B/C/D) C
10476((EXPLANATION)) (OPTIONAL)
10477
10478((MARKS)) (1/2/3...) 1
10479((QUESTION)) The edge connectivity of for a complete Graph K6 on six vertices is
10480((OPTION_A)) 3
10481((OPTION_B)) 5
10482((OPTION_C)) 4
10483((OPTION_D)) 2
10484((CORRECT_CHOICE)) (A/B/C/D) B
10485((EXPLANATION)) (OPTIONAL)
10486
10487((MARKS)) (1/2/3...) 1
10488((QUESTION)) The vertex connectivity for the complete bipartite graph K3,4 is
10489((OPTION_A)) 2
10490((OPTION_B)) 1
10491((OPTION_C)) 3
10492((OPTION_D)) 4
10493((CORRECT_CHOICE)) (A/B/C/D) C
10494((EXPLANATION)) (OPTIONAL)
10495
10496
10497
10498((MARKS)) (1/2/3...) 1
10499((QUESTION)) A path in which every edge of the graph appers exactly once is
10500((OPTION_A)) Hamiltonian
10501((OPTION_B)) Eulerian
10502((OPTION_C)) Hamiltonian Circuit
10503((OPTION_D)) None of these
10504((CORRECT_CHOICE)) (A/B/C/D) B
10505((EXPLANATION)) (OPTIONAL)
10506
10507((MARKS)) (1/2/3...) 1
10508((QUESTION)) A circuit which contains every edge of the graph exactly once is
10509((OPTION_A)) Eulerian circuit
10510((OPTION_B)) Hamiltonian circuit
10511((OPTION_C)) Hamiltonian graph
10512((OPTION_D)) None of these
10513((CORRECT_CHOICE)) (A/B/C/D) A
10514((EXPLANATION)) (OPTIONAL)
10515
10516((MARKS)) (1/2/3...) 1
10517((QUESTION)) A graph which has an Eulerian circuit is
10518((OPTION_A)) Hamiltonian graph
10519((OPTION_B)) Complete bipartite graph
10520((OPTION_C)) Eulerian graph
10521((OPTION_D)) None of these
10522((CORRECT_CHOICE)) (A/B/C/D) C
10523((EXPLANATION)) (OPTIONAL)
10524
10525((MARKS)) (1/2/3...) 1
10526((QUESTION)) A graph possesses an Eulerian circuit if and only if it is connected and has vertices which all have
10527((OPTION_A)) Even degree
10528((OPTION_B)) Odd degree
10529((OPTION_C)) Degree one
10530((OPTION_D)) Degree three
10531((CORRECT_CHOICE)) (A/B/C/D) A
10532((EXPLANATION)) (OPTIONAL)
10533
10534((MARKS)) (1/2/3...) 1
10535((QUESTION)) A path in which every vertex of the graph appears exactly once is
10536((OPTION_A)) Eulerian path
10537((OPTION_B)) Hamiltonian path
10538((OPTION_C)) Eulerian circuit
10539((OPTION_D)) Hamiltonian circuit
10540((CORRECT_CHOICE)) (A/B/C/D) B
10541((EXPLANATION)) (OPTIONAL)
10542
10543((MARKS)) (1/2/3...) 1
10544((QUESTION)) A graph which has Hamiltonian circuit is called
10545((OPTION_A)) Hamiltonian graph
10546((OPTION_B)) Complete bipartite graph
10547((OPTION_C)) Eulerian graph
10548((OPTION_D)) None of these
10549((CORRECT_CHOICE)) (A/B/C/D) A
10550((EXPLANATION)) (OPTIONAL)
10551
10552((MARKS)) (1/2/3...) 1
10553((QUESTION)) A complete graph k4 on four vertices has
10554((OPTION_A)) Eulerian circuit
10555((OPTION_B)) Hamiltonian circuit
10556((OPTION_C)) Neither Eulerian nor Hamiltonian circuit
10557((OPTION_D)) Both Eulerian and Hamiltonian circuit
10558((CORRECT_CHOICE)) (A/B/C/D) D
10559((EXPLANATION)) (OPTIONAL)
10560
10561((MARKS)) (1/2/3...) 2
10562((QUESTION)) How many edges must a planar graph have if it has 7 regions and 5 vertices?
10563((OPTION_A)) 9
10564((OPTION_B)) 10
10565((OPTION_C)) 8
10566((OPTION_D)) 7
10567((CORRECT_CHOICE)) (A/B/C/D) B
10568((EXPLANATION)) (OPTIONAL)
10569
10570((MARKS)) (1/2/3...) 2
10571((QUESTION)) The number of regions defined by a connected planar graph with 6 vertices and 10 edges are
10572((OPTION_A)) 6
10573((OPTION_B)) 7
10574((OPTION_C)) 5
10575((OPTION_D)) 4
10576((CORRECT_CHOICE)) (A/B/C/D) A
10577((EXPLANATION)) (OPTIONAL)
10578
10579((MARKS)) (1/2/3...) 2
10580((QUESTION)) A connected planar graph has nine vertices having 2,2,2,3,3,3,4,4 and 5. The number of regions it has is
10581((OPTION_A)) 6
10582((OPTION_B)) 5
10583((OPTION_C)) 7
10584((OPTION_D)) 9
10585((CORRECT_CHOICE)) (A/B/C/D) C
10586((EXPLANATION)) (OPTIONAL)
10587
10588((MARKS)) (1/2/3...) 1
10589((QUESTION)) The following graph is
10590
10591
10592
10593
10594
10595
10596((OPTION_A)) Planar graph
10597((OPTION_B)) Complete graph
10598((OPTION_C)) Regular graph
10599((OPTION_D)) None of these
10600((CORRECT_CHOICE)) (A/B/C/D) A
10601((EXPLANATION)) (OPTIONAL)
10602
10603((MARKS)) (1/2/3...) 1
10604((QUESTION)) A graph which can be drawn on the plane such that no edges cross each other called
10605((OPTION_A)) Complete
10606((OPTION_B)) Regular
10607((OPTION_C)) Planar
10608((OPTION_D)) Complete bipartite graph
10609((CORRECT_CHOICE)) (A/B/C/D) C
10610((EXPLANATION)) (OPTIONAL)
10611
10612((MARKS)) (1/2/3...) 1
10613((QUESTION)) In the following graph self loop is
10614
10615
10616
10617
10618
10619((OPTION_A)) e1
10620((OPTION_B)) e2
10621((OPTION_C)) e3
10622((OPTION_D)) e4
10623((CORRECT_CHOICE)) (A/B/C/D) A
10624
10625
10626((MARKS)) (1/2/3...) 1
10627((QUESTION)) The following graph is
10628
10629
10630
10631
10632
10633
10634((OPTION_A)) Complete
10635
10636((OPTION_B)) Complete bipartite
10637((OPTION_C)) Bipartite
10638((OPTION_D)) Regular
10639((CORRECT_CHOICE)) (A/B/C/D) B
10640((EXPLANATION)) (OPTIONAL)
10641
10642
10643
10644((MARKS)) (1/2/3...) 2
10645((QUESTION)) The edge connectivity of following graph is
10646
10647
10648
10649
10650
10651((OPTION_A)) 1
10652((OPTION_B)) 2
10653((OPTION_C)) 3
10654((OPTION_D)) 4
10655((CORRECT_CHOICE)) (A/B/C/D) C
10656((EXPLANATION)) (OPTIONAL)
10657
10658((MARKS)) (1/2/3...) 2
10659((QUESTION)) The vertex connectivity of following graph is
10660
10661
10662
10663
10664
10665((OPTION_A)) 1
10666((OPTION_B)) 2
10667((OPTION_C)) 3
10668((OPTION_D)) 4
10669((CORRECT_CHOICE)) (A/B/C/D) B
10670
10671((MARKS)) (1/2/3...) 2
10672((QUESTION)) Consider the following graphs
10673
10674
10675
10676These graphs are
10677((OPTION_A)) Isomorphic
10678((OPTION_B)) Null
10679((OPTION_C)) Non isomorphic
10680((OPTION_D)) Complementary
10681((CORRECT_CHOICE)) (A/B/C/D) C
10682
10683
10684
10685
10686((MARKS)) (1/2/3...) 2
10687((QUESTION)) The following graphs are
10688
10689
10690
10691((OPTION_A)) Complete bipartite
10692((OPTION_B)) Isomorphic
10693((OPTION_C)) Non isomorphic
10694((OPTION_D)) Null graph
10695((CORRECT_CHOICE)) (A/B/C/D) B
10696
10697((MARKS)) (1/2/3...) 2
10698((QUESTION)) The adjacency matrix of the following graph is
10699
10700
10701
10702
10703
10704((OPTION_A))
10705
10706((OPTION_B))
10707
10708((OPTION_C))
10709
10710((OPTION_D))
10711
10712((CORRECT_CHOICE)) (A/B/C/D) A
10713((EXPLANATION)) (OPTIONAL)
10714
10715((MARKS)) (1/2/3...) 2
10716((QUESTION)) Consider a graph G and its sub graph H1 and H2
10717
10718
10719
10720
10721
10722
10723
10724
10725
10726 H1 H2
10727Then H1 and H2 are
10728((OPTION_A)) Vertex disjoint sub graph
10729((OPTION_B)) Edge disjoint sub graph
10730((OPTION_C)) Spanning subgraph
10731((OPTION_D)) None of these
10732((CORRECT_CHOICE)) (A/B/C/D) B
10733((EXPLANATION)) (OPTIONAL)