5k1Ng61w

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4Sr No	Question	Option 1	Option 2	Option 3	Option 4	Correct Option	Marks	Topic	Unit
51	IF p ᴧ q  is T, Then	p is T , q is T	p is F , q is T	p is F, q is F	p is T, q is F	p is F , q is T	1	Preposition	1
62	IF p ᴠ q  is F, Then	p is T , q is F	p is F , q is T	p is F, q is F	p is T, q is F	p is F, q is F	1	Preposition	1
73	IF p ᴠ ~q  is F, Then	p is T , q is F	p is F , q is T	p is F, q is F	p is T, q is F	p is F , q is T	1	Preposition	1
84	IF ~p ᴠ q  is F, Then	p is T , q is F	p is F , q is T	p is F, q is F	p is T, q is F	p is T, q is F	1	Preposition	1
95	IF p -> q  is F, Then	p is T , q is T	p is F , q is T	p is F, q is F	p is T, q is F	p is T, q is F	1	Preposition	1
106	The statement form ~(p ᴠ q) is logically equivalent to	~p ᴠ ~q	~p ᴠ q	p ᴠ ~q	~p ᴧ ~q	~p ᴧ ~q	1	Preposition	1
117	The statement form ~(p ᴧ q) is logically equivalent to	~p ᴠ ~q	~p ᴠ q	p ᴠ ~q	~p ᴧ ~q	~p ᴠ ~q	1	Preposition	1
128	p -> q is logically equivalent to	q -> p	~p ᴧ q	~p ᴠ q	p ᴠ ~q	~p ᴠ q	1	Preposition	1
139	p -> p is logically equivalent to	p	tautology	contradiction	None Of These	tautology	1	Preposition	1
1410	p ᴧ p is logically equivalent to	p	tautology	contradiction	None Of These	p	1	Preposition	1
1511	p ᴠ(p ᴧ q) is logically equivalent to	q	p	tautology	contradiction	p	1	Preposition	1
1612	p ᴧ(p ᴠ q) is logically equivalent to	p	q	p ᴠ q	tautology	p	1	Preposition	1
1713	p ᴧ ~p is logically equivalent to	p	~p	tautology	contradiction	contradiction	1	Preposition	1
1814	p ᴠ p is logically equivalent to	p	~p	tautology	contradiction	contradiction	1	Preposition	1
1915	p ᴠ ~p is logically equivalent to	p	tautology	contradiction	None Of These	p	1	Preposition	1
2016	The converse p->q is	~q -> ~p	~p -> ~q	~p -> q	~q -> p	q -> p	1	Preposition	1
2117	The contrapositive p->q is	~q -> ~p	~p -> ~q	~p -> q	q -> p	~q -> ~p	1	Preposition	1
2218	Let p : mohan is rich, q : mohan is happy then the statement mohan is rich but not happy is 	p ᴧ q	~p ᴧ q	p ᴠ q	p ᴧ ~q	p ᴧ ~q	1	Preposition	1
2319	Let p : its rain, q : I go for walk, then the statement if it rains, I will not go for walk is 	p ᴧ q	p -> q	p -> ~q	q -> p	p -> ~q	1	Preposition	1
2420	Let p : I will get a job, q : I pass exam then the statement form I will get the job only I pass the exam is	p -> q	p ᴧ q	q -> p	p ᴠ q	p -> q	1	Preposition	1
2521	IF q -> ~p is F then	p is T , q is T	p is T, q is F	p is F , q is T	p is F, q is F	p is T , q is T	1	Preposition	1
2622	IF ~p ᴠ q  is F, Then	p is T , q is F	p is F , q is T	p is F, q is F	p is T, q is F	p is T, q is F	1	Preposition	1
2723	p ᴧ p is logically equivalent to	p	tautology	contradiction	None Of These	p	1	Preposition	1
2824	p ᴠ p is logically equivalent to	p	~p	tautology	contradiction	contradiction	1	Preposition	1
2925	Let p : Gopal is tall, q : Gopal is handsome then the statement Gopal is tall but not handsome is	~p ᴧ q	~p ᴠ q	~p ᴠ ~q	~p ᴧ ~q	~p ᴠ q	1	Preposition	1
3026	Let p : It rains heavily, q : I will go for a drive then the converse of statement If it rains heavily I will not go fro a drive	p -> q	q -> p	~q -> p	~q -> ~p	~q -> p	1	Preposition	1
3127	Let R be a non-empty relation on a collection of sets defined by ARB if and only  If  A  ∩ B  Ø Then (pick the TRUE statement)	R is relexive and transitive          	R is symmetric and not transitive	R is an equivalence relation    	R is not relexive and not symmetric	R is symmetric and not transitive	1	Set Theory	1
3228	Let S= {0, 2, 4, 6, 8, _, _, _, _) then S is Called. 	Countable infinite Set. 	Power Set.	Uncountable infinite Set	Multiset.	Countable infinite Set. 	1	Set Theory	1
3329	which of the following sets are null sets?                                                  	{0}                                  	ø	{ }	Both (b) & (c)	Both (b) & (c)	1	Set Theory	1
3430	The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is	2	4	8	None Of These	8	1	Set Theory	1
3531	A partial ordered relation is transitive, reflexive and	antisymmetric.         	bisymmetric.        	antireflexive.        	asymmetric.	antisymmetric.         	1	Set Theory	1
3632	If  A= [1,1,3,3,3,4] and B=[ 1,2,2,4,5,5] then A  ∩ B  is 	[1,1,2]	[1,4]          	[1,2,2,3,3,3,4,5,5] 	[1,2,4]	[1,4]          	2	Set Theory	1
3733	Let N = {1, 2, 3, ….} be ordered by divisibility, which of the following subset   is totally ordered,                                                                                               	(2, 6, 24).             	(3, 5, 15).       	(2, 9, 16).        	(4, 15, 30).	(2, 6, 24).             	2	Set Theory	1
3834	Which of the following proposition is a tautology?	(P v q)®p       	p v (q®p)       	p v (p®q)        	p®(p®q)	p v (p®q)        	2	Set Theory	1
3935	Let P= {a,a,a,b,b,c,d,d,e} and Q= {a,a,b,b,b,c,c,d,d,f} then P –Q	{a,e}          	{ a,b,e}        	{a,b,d,e} 	{a,e,b,d}	{a,e}          	2	Set Theory	1
4036	Which one of the following statement is correct?                          	A Ç B = F = A = F or B = F	A– B = F A Ì B	A Ç B = FA Ì B                        	A Ç B = A D B	A– B = F A Ì B	2	Set Theory	1
4137	The total number of elements in the power set of A containing n elements is	2n	n2  	2n –1                     	22n	2n	2	Set Theory	1
4238	How Many number’s between 1 to 250 that are divisible by integer 2,3,5,7	192	194	191	193	193	4	Set Theory	1
4339	How Many number’s between 1 to 1000 are not divisible by 3 nor by 5, Nor by 7.  	459	457	553	543	457	4	Set Theory	1
4440	p ᴧ p is logically equivalent to	p	tautology	contradiction	None Of These	p	1	Preposition	1
4541	IF p ᴧ (p -> q) is T, then 	p is T, q is F	p is F, q is T	p is T, q is T	p is F , q is F	p is T, q is T	2	Preposition	1
4642	IF (~(p ᴠ q)) -> q is F, then 	p is T, q is F	p is F, q is T	p is T, q is T	p is F , q is F	p is F , q is F	2	Preposition	1
4743	IF (~p -> r) ᴧ (p <-> q) is T and r is F, then truth values of p and q are	p is T, q is T	p is T, q is F	p is F , q is F	p is F, q is T	p is T, q is T	2	Preposition	1
4844	IF ((p -> q) -> q) -> p is F then 	p is T, q is T	p is T, q is F	p is F, q is T	p is F , q is F	p is F, q is T	2	Preposition	1
4945	The disjunctive normal form of (p  ᴠ  ~q) -> q is 	(p ᴧ q) ᴠ p	(~p ᴧ q) ᴠ q	(p ᴧ q) ᴠ p	(p ᴧ ~q) ᴠ q	(~p ᴧ q) ᴠ q	2	Preposition	1
5046	The disjunctive normal form of  p  ᴧ (p -> q) is 	p ᴧ q	(p ᴧ q) ᴠ p	(p ᴠ q) ᴧ q	p ᴠ q	p ᴧ q	2	Preposition	1
5147	p  ᴧ (p -> q) -> q is logically equivalent to 	p ᴠ q	(p ᴧ q) ᴠ (~p ᴧ q)	tautology	p ᴧ q	tautology	2	Preposition	1
5248	The conjuctive normal form of  p  ᴧ (p -> q) is 	p ᴧ q	(p ᴧ q) ᴠ p	(p ᴠ q) ᴧ q	p ᴠ q	p ᴧ q	2	Preposition	1
5349	The premises p, p -> q is logically implies 	q	p	~p	~q	q	2	Preposition	1
5450	The premises p -> q, ~q is logically implies 	q	p	~p	~q	~p	2	Preposition	1
5551	If A and B are non empty sets then 	AƇ A U B	B C A U B	both a and b	none of these	both a and b	1	Set Theory	1
5652	If A and B are non empty sets then 	A Π B Ƈ A and A Π B Ƈ B	A Ƈ A Π B and B Ƈ A Π B 	both a and b	none of these	A Π B Ƈ A and A Π B Ƈ B	1	Set Theory	1
5753	If A and B are two sets then 	|AU B| = |A| + |B| -|AΠB|	|AU B| = |A| + |B| +|AΠB|	|AU B| = |A| + |B| 	|AU B| = |A| - |B| 	|AU B| = |A| + |B| -|AΠB|	1	Set Theory	1
5854	If s is a set containing n elements then number of elements in power set of S i.e. P(s) = -----	n	2n	2ʱ	n²	2ʱ	1	Set Theory	1
5955	If A and B are disjoint  sets then 	 A U B = ɸ	 A U B = A	 A U B = B	 A Π B = ɸ	 A U B = A	1	Set Theory	1
6056	If A and B are two sets then which statement is true?	A -B = { x; xεA and xεB}	A -B = { x; x ɆA  and xεB}	A -B = { x; xε A  and x ɆB}	A -B = { x; xɆ A  and x ɆB}	A -B = { x; xε A  and x ɆB}	1	Set Theory	1
6157	If A and B are two  sets then which statement is true? 	(A - B) and (B - A) are equal sets	(A - B) and (B - A) are disjoint  sets	(A - B) = A 	(B- A ) = B	(A - B) and (B - A) are disjoint  sets	1	Set Theory	1
6258	If A and B are two  sets then which statement is true? 	(A - B) ,  (A Π B) and ( B - A) pairwise disjoint sets	(A - B) U (B - A) =  (A Π B)	(A - B) Π  (B - A) =  (A Π B)	(A - B) U  (B - A) =  (A U B)	(A - B) ,  (A Π B) and ( B - A) pairwise disjoint sets	1	Set Theory	1
6359	If A and B are two  sets then which statement is true? 	(A - B) Π  ( A Π B) Π ( B - A) =  (A U B)	(A - B) U  ( A Π B) U ( B - A) =  (A U B)	(A - B) U  ( A Π B) U ( B - A) =  (A ΠB)	(A - B) Π  ( A U B) Π ( B - A) =  (A ΠB)	(A - B) U  ( A Π B) U        ( B - A) =  (A U B)	1	Set Theory	1
6460	If A and B are two sets then symmetric difference of A and B is  	( A U B ) U (A Π B ) 	( A U B )  Π  (A Π B ) 	( A U B )  -  (A Π B ) 	( A Π B )  -  (A U B ) 	( A U B )  -  (A Π B ) 	1	Set Theory	1
6561	If complement of set A is A' and X is universal set then 	A '  = { x; xε X and  xε A}	A '  = { x; x Ɇ X and  x Ɇ A}	A '  = { x; x Ɇ X and  x ε  A}	A '  = { x; x ε X and  x Ɇ A}	A '  = { x; x ε X and  x Ɇ A}	1	Set Theory	1
6662	If A and B are two sets and A ≠ B such that A Π B = A then 	A Ƈ B 	B C A 	both a and b	none of these	A Ƈ B 	1	Set Theory	1
6763	If A and B are two sets and A ≠ B such that A U B = A then 	AƇ  B	B C A 	both a and b	none of these	B C A 	1	Set Theory	1
6864	If A = { 1, 2, 3, 4, 5 }  B = { 3,5,9,6,8 } then A- B =  	{1,2,3,4,5,6,8,9}	{1,2,4}	{9,6,8}	{3,5}	{1,2,4}	2	Set Theory	1
6965	If A , B and C any sets then under what condition the following statement is true. (A-B) U (A-C) = A 	A Π B = ɸ , A Π C= ɸ 	A C B and A C C	B = C 	none of these	A Π B = ɸ , A Π C= ɸ 	2	Set Theory	1
7066	( A U B ) ' = 	A' U B'	A' Π B' 	A U B' 	A' U B	A' Π B' 	1	Set Theory	1
7167	( A Π  B ) ' = 	A' U B'	A' Π B' 	A Π B' 	A' Π B	A' U B'	1	Set Theory	1
7268	For sets A and B , ( A  Π  B) U A = 	A	B	A Π B 	none of these	A	1	Set Theory	1
7369	For sets A and B , ( A  Π  B) Π A = 	A	B	AΠB	none of these	AΠB	1	Set Theory	1
7470	If ɸ is empty set and A is any set and X is universal set then A U ɸ = 	A	ɸ	X	none of these	A	1	Set Theory	1
7571	For sets  A and B,( A U B ) U A =  	 A U B	 A	B	none of these	 A U B	1	Set Theory	1
7672	For sets A and B , ( A U B) Π A = 	 A U B	B 	A	none of these	A	1	Set Theory	1
7773	If X is universal set, ɸ is empty set and A is any set then A Π X = 	A	X	ɸ	none of these	ɸ	1	Set Theory	1
7874	If X is universal set, ɸ is empty set and A is any set then A U X = 	A	X	ɸ	none of these	X	1	Set Theory	1
7975	If X is universal set, ɸ is empty set and A is non empty set then A Π ɸ = 	A	X	ɸ	none of these	ɸ	1	Set Theory	1
8076	If X is universal set, ɸ is empty set and A is non empty set then A Π ɸ = 	ɸ	A	X	none of these	A	1	Set Theory	1
8177	If A' is complement of set A, X is universal set and  ɸ is empty set then A U A' = 	A	A' 	ɸ	X	X	1	Set Theory	1
8278	If A' is complement of set A, X is universal set and  ɸ is empty set then A Π A' = 	A	A' 	ɸ	X	ɸ	1	Set Theory	1
8379	If A = {a,b,{a,c},ɸ} then A - {a,c} = 	{a,b,ɸ}	{b,{a,c},ɸ}	{a,b,{a,c},ɸ}	none of these	{b,{a,c},ɸ}	1	Set Theory	1
8480	for any three non empty sets A,B,C |AUBUC|= 	|A|+|B|+|C|+|A ΠB|+|A ΠC|+|B Π C|+|A ΠB  ΠC|	|A|+|B|+|C|-|A ΠB|-|A ΠC|-|B Π C|-|A ΠB  ΠC|	|A|+|B|+|C|-|A ΠB|-|A ΠC|-|B Π C|+|A ΠB  ΠC|	|A|+|B|+|C|	|A|+|B|+|C|-|A ΠB|-|A ΠC|-|B Π C|+|A ΠB  ΠC|	1	Set Theory	1
85	                                                                                                                                                       X is universal set ɸ is empty set and A is non empty set 								1
8681	if A' Π X = ɸ then 	A = X	A = ɸ	A' = X 	none of these	A = X	1	Set Theory	1
8782	if (A Π B ) ' = B ' then 	A C B	B C A	A U B = B	none of these	B C A	1	Set Theory	1
8883	for any two non empty sets A and B which statement is true? 	A = (A - B) U ( A ΠB) 	A = (B - A) U ( A Π B ) 	A = ( A- B) U ( B - A) 	A = ( A - B) Π ( A Π B) 	A = (A - B) U ( A ΠB) 	1	Set Theory	1
8984	for any two sets  A and B which statement is true?  	B = (A - B) U ( A ΠB) 	B = (B - A) U ( A ΠB) 	B = (A - B) U ( B-A ) 	B = (B - A) Π ( A ΠB) 	B = (B - A) U ( A ΠB) 	1	Set Theory	1
9085	If A = {{a,b}} then which statement is true?	A ε A	a ε A	{a,b} ε A	A has 2 elements	{a,b} ε A	1	Set Theory	1
9186	If A = { 1, 2, 3, 4, 5 }  , B = { 2,3,4 } then  which statement is true?	BεA	A εB	A C B	B C A	B C A	1	Set Theory	1
9287	for any non empty set A , which stetement is true?	a has no subset	A has at least 1 subset	A has atleast 2 subsets	none of these	A has atleast 2 subsets	1	Set Theory	1
9388	If A = {a,b,c{a,b,c}} then which statement is false?	(a,b} ε A	{a,b} C A	{a,b,c} ε A	{a,b,c} C A	(a,b} ε A	1	Set Theory	1
9489	for empty set ɸ which statement is false?	ɸ C ɸ	ɸ ε ɸ	ɸ C {ɸ } 	ɸε ɸ 	ɸ ε ɸ	1	Set Theory	1
9590	if S = {1,2} , P(s) = {ɸ, {1},{2},{1,2}} which statement is false?	ɸ C P ( S) 	ɸε P(S) 	{{1}} ε P(S)	{1} ε P(S)	{{1}} ε P(S)	1	Set Theory	1
96If A = { 1,2,3,4}   ,  B = { 4,5,6,7} then 								Set Theory	1
9791	 A -B is	{ 1,2,3,4,5,6,7}	{5,6,7}	{1,2,3}	{4}	{1,2,3}	1	Set Theory	1
9892	 B -A is	{ 1,2,3,4,5,6,7}	{5,6,7}	{1,2,3}	{4}	{5,6,7}	1	Set Theory	1
9993	 A Π B is	{ 1,2,3,4,5,6,7}	{5,6,7}	{1,2,3}	{4}	{4}	1	Set Theory	1
10094	A U B is	{ 1,2,3,4,5,6,7}	{5,6,7}	{1,2,3}	{4}	{ 1,2,3,4,5,6,7}	1	Set Theory	1
101consider  a set S of integers from 1 to 250. A denotes the set of integers divisible by 3, B denotes the set of integers divisible by 5 and C denotes the set of integers divisible by 7 then 									
10294	| A | is 	125	50	83	35	83	2	Set Theory	1
10395	|B | is	125	50	83	35	50	2	Set Theory	1
10496	| C | is 	125	50	83	35	35	2	Set Theory	1
10597	| A Π B| is  	50	83	16	35	16	2	Set Theory	1
10698	| A Π C | is 	16	11	7	35	7	2	Set Theory	1
10799	| B Π C| is 	16	11	7	35	11	2	Set Theory	1
108100	| A Π B Π C| 	16	11	7	1	1	4	Set Theory	1
109101	| A U B U C |	83	50	35	135	135	4	Set Theory	1
110102	number of elements divisible by 3 or 5 but not by 7	135	100	35	117	100	4	Set Theory	1
111If 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 diisible by 7 , then 									
112103	| A| is --------	2000	1000	666	400	1000	1	Set Theory	1
113104	| B| is -----------	2000	1000	666	400	666	1	Set Theory	1
114105	|C| is -------	1000	666	400	285	400	1	Set Theory	1
115106	|D| is ------------	1000	666	400	285	285	1	Set Theory	1
116107	|A Π B| is ---------	400	285	333	142	333	1	Set Theory	1
117108	|A Π C| is ---------	200	333	142	133	200	1	Set Theory	1
118109	|A Π D| is ---------	142	133	95	57	142	2	Set Theory	1
119110	|B Π D| is ---------	142	57	95	133	95	2	Set Theory	1
120111	|B Π C| is ---------	142	57	95	133	57	2	Set Theory	1
121112	|C Π D| is ---------	142	57	95	133	57	2	Set Theory	1
122113	| A Π B Π C| is--------	57	66	47	28	66	2	Set Theory	1
123114	| A Π B Π D|  is ---------	66	47	28	19	47	2	Set Theory	1
124115	| A Π C Π D| is -----------	66	47	28	19	28	4	Set Theory	1
125116	| B Π C Π D| is -----------	66	47	28	19	19	4	Set Theory	1
126117	| A Π B Π C Π D| is--------	47	19	9	19	9	4	Set Theory	1
127118	| A U B U C U D| is--------	2351	1542	960	160	1542	4	Set Theory	1
128	Among 100 students, 32 study maths, 20 study physics, 45 study biology, 15 study maths and biology, 7 study maths and physics, 10 study physics and biology, and 30 do not study any of the three subjects. 								
129119	number of students studying all three subjects?	7	10	5	30	5	2	Set Theory	1
130120	number of students studying only maths----	7	10	15	8	15	2	Set Theory	1
131121	number of students studying only physics----	15	8	25	10	8	2	Set Theory	1
132122	number of students studying only biology----	15	8	25	10	25	2	Set Theory	1
133123	number of students studying exactly one subject - ---------	25	30	48	70	48	2	Set Theory	1
134124	If A is a finite set of size n, the number of elements in the power set of A X A is -------	2 ² ʱ	2 ʱ ²	  ( 2 ʱ)  ²	none of these	2 ʱ ²	2	Set Theory	1
135125	the number of elements in the power set P(S) of the set S = {{ɸ} , a, {b,c} } is -------	2	4	8	none of these	8	2	Set Theory	1
136126	if A = { X : X²-4X+3 = 0} , B = { X : X² - 3X +2 = 0} , C = {1,2} , D= { 1,3} then -----------	A = C and B = D	A = D and B = C	A = D but B ≠ C	A ≠ D but B = C	A = D and B = C	2	Set Theory	1
137127	if A' is complement of Set A and B' is complement of set B and A C B then ------------	A' C B'	B' C A'	A' = B'	none of these	B' C A'	2	Set Theory	1
138128	if B' is complement of set B and A C B, X is universal set then ------------	A Π B' = ɸ	A Π B' = X	A Π B' = A	none of these	A Π B' = ɸ	2	Set Theory	1
139129	if A' is complement of Set A and A C B and X is universal set  then ------------	A' U B = ɸ 	A' U B = X 	A' U B = B	A' U B = A	A' U B = X 	2	Set Theory	1
140130	There are many clouds in the sky but it did not rain  P : there are many clouds in the sky   q: it rain	P V q	P ʌ q	p V ( ~ q) 	p ʌ (~q) 	p ʌ (~q) 	2	Set Theory	1
141131	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	( P ʌ q) <-> r	( P ʌ r) <-> q	p <-> ( qʌ r) 	q <-> p	p <-> ( qʌ r) 	2	Set Theory	1
142132	computers are cheap but softwares are costly p: computers are cheap,     q: softwares are costlt	P V q	P ʌ q	p V ( ~ q) 	p ʌ (~q) 	P ʌ q	4	Set Theory	1
143133	it is very hot and humid or ramesh is having heart problem p: it is very hot   q: it is very humid,      r: ramesh is having heart problem	p ʌ q ʌ r	( pV q) ʌ r	( P ʌ q) V r	p V r V r	( P ʌ q) V r	4	Set Theory	1
144134	in small restaurants the food is good and service is poor. P : in small restaurants food is good   q: service is poor then--------	p ʌ q	p V q	(~ p ) ʌ q	p ʌ (~q) 	p ʌ q	4	Set Theory	1
145135	Let A = {2, {4, 5}, 4}. Which statement is correct?	 5 is an element of A.	 {5} is an element of A.	 {4, 5} is an element of A.	 {5} is a subset of A. 	 {4, 5} is an element of A.	1	SET 	1
146136	Which of these sets is finite?	 {x | x is even}	 {x | x < 5}	{1, 2, 3,...}	 {1, 2, 3,...,999,1000}	 {1, 2, 3,...,999,1000}	1	SET 	1
147137	Which of these sets is not a null set?	 A = {x | 6x = 24 and 3x = 1}	 B = {x | x + 10 = 10}	 C = {x | x is a man older than 200 years}	 D = {x | x < x}	 B = {x | x + 10 = 10}	1	SET 	1
148138	Let D      E. Suppose a        D and b      E. which of the following statements must be true.	c    D	b    D	a    E	a    D	a    E	1	SET 	1
149139	Let A = {x | x is even}, B = {1, 2, 3,..., 99, 100}, C = {3, 5, 7, 9}, D = {101, 102} and E = {101, 103, 105}. Which of these sets can equal S if S A and S and B are disjoint? 	 A         	 B 	 C 	 E	 E	1	SET 	1
150140	Which set S does the power set 2S = {         , {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} come from?	a) {{1},{2},{3}}	b) {1, 2, 3}	c) {{1, 2}, {2, 3}, {1, 3}}	d) {{1, 2, 3}} 	d) {{1, 2, 3}} 	1	SET 	1
151141	Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct? 	a) A       B = {v, w, x, y, z} 	b) A         B = {v, w, y, z} 	c) A      B = {v, w, x, y} 	d) A        B = {x, w, x, y, z} 	a) A       B = {v, w, x, y, z} 	1	SET 	1
152142	Let A = {1, 2, 3, ..., 8, 9} and B = {3, 5, 7, 9}. Which of the following statements is correct?. 	a) A          B = {2, 4, 6} 	b) A         B = {1, 2, 3, 4, 5, 6, 7, 8, 9} 	c) A        B = {1, 2, 4, 6, 8} 	d) A           B = {2, 4, 6, 8} 	d) A           B = {2, 4, 6, 8} 	1	SET 	1
153143	. Let A = {2, 3, 4}, B = {3} and C = {x | x is even}. Which statement is correct? 	a) C         A=B	b) C          B=A	c) A         C	d) C / A = B 	a) C         A=B	1	SET 	1
154144	Let A          B, B         C and D        A = C. Which statement is always false? 	a) B       D	b) A          C	c) A = B 	d) B       D=           AND B          A	d) B       D=           AND B          A	1	SET 	1
155145	 What is shaded in the Venn diagram below?. 	a) A       B	b) A' 	c) A - B 	d) B - A 	d) B - A 	1	SET 	1
156146	Let U = {1, 2, 3, ..., 8, 9} and A = {1, 3, 5, 7}. Find A'. 	a) A' = {2, 4, 6, 8} 	b) A' = {2, 4, 6, 8, 9} 	c) A' = {2, 4, 6} 	d) A' = {9}	b) A' = {2, 4, 6, 8, 9} 		SET 	1
157147	If a statement is P: I went to my class yesterday. Then ┐P is ___________.	a. i did not go to my class yesterday.	b. i was absent to my class today.	c. it is not the case that I went to my class today.	d. i will not go to class today.	a. i did not go to my class yesterday.	1	Set Theory	1
158148	 If the truth value of P is false then the truth value of negation P is ________.	a. true.	b. false.	c. true or false.	d. true and false.	a. true.	1	Set Theory	1
159149	The conjunction of the statement is formed by introducing _________.	a. OR.	b. NOT.	c. AND.	d. IF.	c. AND.	1	Set Theory	1
160150	If the statements are given by P: It is raining today, Q: There are 20 tables in this room then P ٨Q is ______________.	a. if it is raining today then there are 20 tables in this room.	b. it is raining today and there are 20 tables in this room.	c. it is raining today or there are 20 tables in this room.	d. it is raining today but there are 20 tables in this room.	b. it is raining today and there are 20 tables in this room.	1	Set Theory	1
161151	If the statements are given by P: It is raining today, Q: London is a city. Then P^ ┐Q is ____________.	a. it is raining today and London is a city.	b. it is raining today but London is not a city.	c. it is raining today and London is not a city.	d. if it is raining today then London is not a city.	c. it is raining today and London is not a city.	1	Set Theory	1
162152	If the statement P has the truth value T and Q has the truth value F then P٧Q is ___.	a. T.	b. F.	c. T and F.	d. None.	b. F.	1	Set Theory	1
163153	If the statement P has the truth value T and Q has the truth value F then P٨Q is ___.	a. T.	b. F.	c. T and F.	d. None.	b. F.	1	Set Theory	1
164154	The negation of ┐ (P ٨ Q)٧ R is __________.	a. ┐(P ٨ Q)٨ R.	b. ┐(P ٧ Q)٧ R.	c. ┐(P ٨ Q)٧┐R.	d. (P ٨ Q)٧ R.	c. ┐(P ٨ Q)٧┐R.	1	Set Theory	1
165155	The negation of (P٨Q)٧(Q٨R) is _________.	a. ┐ (P٨Q)٧┐(Q٨R).	b. ┐(P٨Q)٨┐(Q٧R).	c. ┐ (P٧Q)٨┐(Q٨R).	d. ┐(P٨Q)٧┐(Q٧R).	a. ┐ (P٨Q)٧┐(Q٨R).	1	Set Theory	1
166156	For every possible truth values of P, the truth value of P٨┐P is __________.	a. T.	b. F.	c. T and F.	d. None.	b. F.	1	Set Theory	1
167157	Which of the following statement is tautology?	a. (P ٨ Q)٧ Q.	b. (P ٧ Q)٨ Q.	c. (P ٧ Q)٨ ┐P.	d. (P ٧ Q)٧┐P.	d. (P ٧ Q)٧┐P.	1	Set Theory	1
168158	The symbolic form for the statement, Mark is poor or he is both rich and unhappy is __________.	a. ┐R٧(R٨┐H).	b. R٨┐(R٨┐H).	c. ┐R٧ (R٧┐H).	d. ┐R٨ (R٨┐H).	a. ┐R٧(R٨┐H).	1	Set Theory	1
169159	The conditional statement is formed by introducing ____________.	a. P and Q.	b. P or Q.	c. P if and only if Q.	d. If P then Q.	d. If P then Q.	1	Set Theory	1
170160	The Bi-conditional statement is formed by introducing ________.	a. P and Q.	b. P or Q.	c. P if and only if Q.	d. If P then Q.	c. P if and only if Q.	1	Set Theory	1
171161	If P has the truth value t and Q has truth value F then P→Q is __________.	a. T.	b. F.	c. T or F.	d. T and F.	b. F.	1	Set Theory	1
172162	Which one of the following statement is example of P→Q?	a. the sun is shining today but 2+7>4.	b. if the sun is shining today, then 2+7>4.	c. the sun is shining today and 2+7>4.	d. the sun is shines today if and only if 2+7>4.	b. if the sun is shining today, then 2+7>4.	1	Set Theory	1
173163	Which one of the following is the example of P↔Q?	a. the sun is shining today but 2+7>4.	b. if the sun is shining today, then 2+7>4.	c. the sun is shining today and 2+7>4.	d. the sun is shines today if and only if 2+7>4.	d. the sun is shines today if and only if 2+7>4.	1	Set Theory	1
174164	P is equivalent to __________.	a. ┐┐P.	b. P٧P.	c. P٨P.	d. Both (a) and (b).	a. ┐┐P.	1	Set Theory	1
175165	(P٨┐P)٧P is equivalent to ____________.	a. P.	b. Q.	c. ┐P.	d. ٧Q.	b. Q.	1	Set Theory	1
176166	P٧┐P is equivalent to ___________.	a. ┐P٧┐P.	b. P٨┐P.	c. Q٧┐Q.	d. Q٨┐Q.	c. Q٧┐Q.	1	Set Theory	1
177167	Which one of the following is well formed formula?	a. (P→Q) →(٨Q).	b. (P٨Q)→Q.	c. (P٨Q)→Q).	d. ((P٨Q)→Q).	b. (P٨Q)→Q.	1	Set Theory	1
178168	Which of the following statement is the negation of the statement, “2 is even and –3 is negative”?	a 2 is even and –3 is not negative.	b. 2 is odd and –3 is not negative.	c. 2 is even or –3 is not negative.	d. 2 is odd or –3 is not negative.	d. 2 is odd or –3 is not negative.	1	Set Theory	1
179169	A partial ordered relation is transitive, reflexive and	a antisymmetric. 	b. bisymmetric.	c. antireflexive.	d. asymmetric.	a antisymmetric. 	1	Set Theory	1
180170	If A and B are disjoint  sets then 	 A U B = ɸ	 A U B = A	 A U B = B	 A Π B = ɸ	 A U B = A	1	Set Theory	1
181171	Which of the following statements is TRUE?	a. For all sets A, B, and C, A − (B − C) = (A − B) − C.	b. For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.	c. For all sets A, B, and C, (A − B) ∩ (C − B) = A − (B U C).	d. For all sets A, B, and C, if A ∩ C = B ∩ C then A = B.	b. For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.	1	Set Theory	1
182172	If a statement is P: I went to my class yesterday. Then ┐P is ___________.	a. i did not go to my class yesterday.	b. i was absent to my class today.	c. it is not the case that I went to my class today.	d. i will not go to class today.	a. i did not go to my class yesterday.	1	Set Theory	1
183173	 If the truth value of P is false then the truth value of negation P is ________.	a. true.	b. false.	c. true or false.	d. true and false.	a. true.	1	Set Theory	1
184174	The conjunction of the statement is formed by introducing _________.	a. OR.	b. NOT.	c. AND.	d. IF.	c. AND.	1	Set Theory	1
185175	If the statements are given by P: It is raining today, Q: There are 20 tables in this room then P ٨Q is ______________.	a. if it is raining today then there are 20 tables in this room.	b. it is raining today and there are 20 tables in this room.	c. it is raining today or there are 20 tables in this room.	d. it is raining today but there are 20 tables in this room.	b. it is raining today and there are 20 tables in this room.	1	Set Theory	1
186176	If the statements are given by P: It is raining today, Q: London is a city. Then P^ ┐Q is ____________.	a. it is raining today and London is a city.	b. it is raining today but London is not a city.	c. it is raining today and London is not a city.	d. if it is raining today then London is not a city.	c. it is raining today and London is not a city.	1	Set Theory	1
187177	If the statement P has the truth value T and Q has the truth value F then P٧Q is ___.	a. T.	b. F.	c. T and F.	d. None.	b. F.	1	Set Theory	1
188178	If the statement P has the truth value T and Q has the truth value F then P٨Q is ___.	a. T.	b. F.	c. T and F.	d. None.	b. F.	1	Set Theory	1
189179	The negation of ┐ (P ٨ Q)٧ R is __________.	a. ┐(P ٨ Q)٨ R.	b. ┐(P ٧ Q)٧ R.	c. ┐(P ٨ Q)٧┐R.	d. (P ٨ Q)٧ R.	c. ┐(P ٨ Q)٧┐R.	1	Set Theory	1
190180	The negation of (P٨Q)٧(Q٨R) is _________.	a. ┐ (P٨Q)٧┐(Q٨R).	b. ┐(P٨Q)٨┐(Q٧R).	c. ┐ (P٧Q)٨┐(Q٨R).	d. ┐(P٨Q)٧┐(Q٧R).	a. ┐ (P٨Q)٧┐(Q٨R).	1	Set Theory	1
191181	For every possible truth values of P, the truth value of P٨┐P is __________.	a. T.	b. F.	c. T and F.	d. None.	b. F.	1	Set Theory	1
192182	Which of the following statement is tautology?	a. (P ٨ Q)٧ Q.	b. (P ٧ Q)٨ Q.	c. (P ٧ Q)٨ ┐P.	d. (P ٧ Q)٧┐P.	d. (P ٧ Q)٧┐P.	1	Set Theory	1
193183	The symbolic form for the statement, Mark is poor or he is both rich and unhappy is __________.	a. ┐R٧(R٨┐H).	b. R٨┐(R٨┐H).	c. ┐R٧ (R٧┐H).	d. ┐R٨ (R٨┐H).	a. ┐R٧(R٨┐H).	1	Set Theory	1
194184	The conditional statement is formed by introducing ____________.	a. P and Q.	b. P or Q.	c. P if and only if Q.	d. If P then Q.	d. If P then Q.	1	Set Theory	1
195185	The Bi-conditional statement is formed by introducing ________.	a. P and Q.	b. P or Q.	c. P if and only if Q.	d. If P then Q.	c. P if and only if Q.	1	Set Theory	1
196186	If P has the truth value t and Q has truth value F then P→Q is __________.	a. T.	b. F.	c. T or F.	d. T and F.	b. F.	1	Set Theory	1
197187	Which one of the following statement is example of P→Q?	a. the sun is shining today but 2+7>4.	b. if the sun is shining today, then 2+7>4.	c. the sun is shining today and 2+7>4.	d. the sun is shines today if and only if 2+7>4.	b. if the sun is shining today, then 2+7>4.	1	Set Theory	1
198188	Which one of the following is the example of P↔Q?	a. the sun is shining today but 2+7>4.	b. if the sun is shining today, then 2+7>4.	c. the sun is shining today and 2+7>4.	d. the sun is shines today if and only if 2+7>4.	d. the sun is shines today if and only if 2+7>4.	1	Set Theory	1
199189	P is equivalent to __________.	a. ┐┐P.	b. P٧P.	c. P٨P.	d. Both (a) and (b).	a. ┐┐P.	1	Set Theory	1
200190	(P٨┐P)٧P is equivalent to ____________.	a. P.	b. Q.	c. ┐P.	d. ٧Q.	b. Q.	1	Set Theory	1
201191	P٧┐P is equivalent to ___________.	a. ┐P٧┐P.	b. P٨┐P.	c. Q٧┐Q.	d. Q٨┐Q.	c. Q٧┐Q.	1	Set Theory	1
202192	Which one of the following is well formed formula?	a. (P→Q) →(٨Q).	b. (P٨Q)→Q.	c. (P٨Q)→Q).	d. ((P٨Q)→Q).	b. (P٨Q)→Q.	1	Set Theory	1
203193	Which of the following statement is the negation of the statement, “2 is even and –3 is negative”?	a 2 is even and –3 is not negative.	b. 2 is odd and –3 is not negative.	c. 2 is even or –3 is not negative.	d. 2 is odd or –3 is not negative.	d. 2 is odd or –3 is not negative.	1	Set Theory	1
204194	A partial ordered relation is transitive, reflexive and	a antisymmetric. 	b. bisymmetric.	c. antireflexive.	d. asymmetric.	a antisymmetric. 	1	Set Theory	1
205
206
2071) The proposition ~pvq is equivalent to 
208A. p ->q        B. q->p      C. p ^ q    D. p v q
209
2102) p->q is logically equivalent to
211A. ~ q -> p    B. ~ p->q     C. ~ p ^ q    D. ~ p v q
212
2133) 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:
214A. p ^ q     B. ~ (~ p v q)     C. p v ~ q     D. ~ p ^ q
215
216
2174) Which of the following set is null set?
218A. {0}       B. { }        C. {Φ}   D.  Φ
219
2205. Which of the following proposition is a tautology?
221A. (p v q) -> p         B. p v (q->p)   C. p v (p->q)  D. p->(p->q)
222
2236. Which one is the contrapositive of q -> p ?
224A. p -> q      B. ¬p -> ¬q    C. ¬q -> ¬p  D. None of these
225
2267. Which of the following statement is the negation of the statement,“2 is even and –3 is negative”?
227A. 2 is even and –3 is not negative.
228B. 2 is odd and –3 is not negative.
229C. 2 is even or –3 is not negative.
230D. 2 is odd or –3 is not negative.
231
2328 . if A = { F, a} , then A n p(A) is 
233A. F    B. A      C. p(A)     D. { F }
234
235 9. If A is the set containing 5 distinct element then cardinality of the power set of A is
236A. 64    B. 16  C. 32   D. 128
237
23810. if pvq is F then
239A. p is T and q is T        B. p is T and q is F
240C. p is F and q is F         D. p is F and q is T
241
24211. The converse of  p -> q is 
243A. ¬q -> ¬p    B. ¬p -> ¬q   C.  ~p -> q  D.  q -> p
244
245
24612. p v ( p ^ q )is logically equivqlnt to
247A. q    B.  p    C. contradiction   D. tautology
248
249
25013. The negation of the statement for all x |x|= x, is
251A. for all x |x| is not equal to x
252B. there exist x,|x| is not equal to x
253C. there exist x,|x| is  equal to x
254D. None of these
255
25614. The cardinality of set A= { 1,1,2,2,2,3,3,3,4,5,5,6,6,6,6,7 } is
257A. 10   B. 16      C. 7 D. none of these
258
25915. If A and B are sets and A U B = A  ∩ B, then
260A. A = Φ   B. B = Φ      C. A = B   D. none of these 
261
26216. Let A={2,{4,5},4} Which statement is correct?
263
264A. 5 is an element of A.         B. {5} is an element of A
265C. {4, 5} is an element of A     D. {5} is a subset of A 
266
26717. Which of these sets is finite?
268
269A. {x | x is even}   B.  {1, 2, 3,...}   C. {1, 2,3,...,999,1000}
270D. none
271
27218. Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct?
273A. A U B ={v,w,x,y,z}  B.  A U B ={v,w,y,z}   C. A U B ={v,w,x,z}
274D. none
275
27619. which sets are equal ? 1.{r,s,t} 2.{s,s,t,r} 3.{t,r,t,s}
277A. 1 and 2     B.  1 and 3      C. 3 and 2   D. ALL ARE EQUAL 
278
27920. If U = {1, 2, 3, . . . 10 } and S = { 4, 5, 6, 7, 8 }, then S ' =
280A. { 9, 10 }    B.  {1, 2, 3 } C. {1, 2, 3 9 } D. {1, 2, 3 9 10 }
281
28221. Which of the following proposition is a tautology?
283A. (p v q) -> p
284B. p v (q->p)
285C. p v (p->q) 
286D. p->(p->q)
287
28822. The difference set A-B is equal to
289A. A n ~B
290B. ~A n B
291C. ~A n ~ B
292D. ~A
293
29423. The set ( A-B ) - C is equal to the set
295A. ( A-B ) n C
296B. ( A U B ) -C
297C. ( A-B )U C 
298D.  A - ( B U C )
299
30024. Among the integers 1 to 300 which are divisible by 3 or 5 is 
301A. 100      B. 60    C. 80   D. 140
302
30325. if ( p v q ) ^ (~ p v ~q ) is F then 
304A. p is T , q is T or q is F
305B. p is F , q is T
306C. p is T , q is F
307D. p and q must have same truth values.
308
309
31026. Find the number of subsets of the set, A={x | x is a day of the week}
311A. 127   B. 128     C. 256    D. 124
31227. Let P= (a,a,a,b,b,c,c,d} and Q={ a,a,b,c,d,e,f,f} then P U Q is 
313A. {a,a,a,a,a,b,b,b,c,c,c,d,d,,e,f,f}
314B. {a,a,b,c,d,e,f}
315C. {a,b,c}
316D. {a,a,a,b,b,c,c,d,e,f,f}
317
31828. Let S={1, 2, 3}. How many subsets does S contain?
319A. 3      B.  6    C. 8   D. 4
320
32129. The number of elements in the power set P(S) of the set S={{Ф},1,{1,2,3} is
322A. 2    B.  4     C. 8    D. NONE
323
32430. If A and B are any two sets, then A ∩ (A ∪ B) is equal to
325
326A. B       B.  AUB    C. BUA   D. A
327
32831. [~ q ^ (p→q)]→~ p is
329A.Satisfiable      B. tautology  C. unsatisfiable D.  contradiction
330
33132. The statement ( p^q) → p is a
332
333A.contadiction   B. tautology  C. Satisfiable  D. Contingency
334
33533. 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: 
336A.  p ^ q    B.  ~ (~ p ^q)  C.  p^ ~ q   D.  ~ p ^q
337
338
33934. 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? 
340A. 564   B. 645   C.  756   D. None of these
341
34235. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
343A. 210   B. 1050   C.  25200 D. None of these
344
345
34636. 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? 
347A. 32  B. 48   C. 64  D. None of these
348
34937. 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?
350A. 40  B. 400  C. 5040 D. None of these
351
35238.  In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? 
353A. 120  B. 720  C. 756 D. None of these
354
35539. In how many ways can the letters of the CHEATER be arranged
356A. 2520    B. 360  C. 756 D. None of these
357
35840 In how many way the letter of the word "RUMOUR" can be arranged
359A. 360   B. 180   C. 280 D. None of these
3601. Number of edges necessary to construct graph with exactly 6 edges in which each node of degree 2 is 
361A. 2                B. 4          C. 6                 D. None 
362
3632. number of edges in graph with 6 nodes of degree, 2 of degree 4 and 4 of degree 2 is 
364A. 4            B. 6               C. 8             D. None 
365 
3663. Number of edges in K10 
367A. 45                B. 40          C. 5        D. None 
368
3694. Number of edges in K5,7 
370A. 45            B. 40         C. 35         D. None 
371 
3725. Number of non-isomorphic graph possible on 2 vertices are 
373A. 2             B. 3               C. 1      D. None of these 
374 
3756. Number of non-isomorphic graph possible on 3 vertices are 
376A. 2            B. 3          C. 4      D. None of these 
377
3787. Complement of K3,2 IS 
379A. connected graph     B. complete graph     C. regular graph  D. not a regular graph 
380 
3818. Edge connectivity of complete graph K5 is 
382A. 2        B. 3       C. 4       D. 5 
383 
3849. Vertex connectivity & Edge connectivity of K4,3 is 
385A. 2         B. 3       C. 4        D. 5 
386 
38710. Vertex connectivity & Edge connectivity of K7,6 is 
388A. 5        B. 6      C. 7      D. 8 
389 
39011. Vertex connectivity & Edge connectivity of K8,9 is 
391A. 8      B. 6        C. 9    D. 7 
392 
39312. the value of n FOR which complete gaph Kn on n nodes contains euler circuit 
394A. odd      B. even      C. n-1  D. n*n 
395 
39613. K1,3 has 
397A. Euler path           B. Euler circuit   C. Hamiltonian path & circuit  D. None of these 
398
39914. Number of regions in K4 
400A. 4       B. 3       C. 2       D. 5
401
402
403
404
405
406C 
407C
408A
409C
410A
411C
412D
413C
414B
415B
416A
417A
418D
419D
420
421
422Which of the following proposition is a tautology?
423A. (p v q) -> p
424B. p v (q->p)
425C. p v (p->q) 
426D. p->(p->q)
427Answer: C
428
429The difference set A-B is equal to
430A. A n ~B
431B. ~A n B
432C. ~A n ~ B
433D. ~A
434Answer: A
435
436The set ( A-B ) - C is equal to the set
437A. ( A-B ) n C
438B. ( A U B ) -C
439C. ( A-B )U C 
440D.  A - ( B U C )
441Answer: D
442
443Among the integers 1 to 300 which are divisible by 3 or 5 is 
444A. 100
445B. 60
446C. 80
447D. 140
448Answer: C
449
450if ( p v q ) ^ (~ p v ~q ) is F then 
451A. p is T , q is T or q is F
452B. p is F , q is T
453C. p is T , q is F
454D. p and q must have same truth values.
455Answer: D
456
457Find the number of subsets of the set, A={x | x is a day of the week}
458A. 127
459B. 128
460C. 256
461D. 124
462Answer: B
463
464Let P= (a,a,a,b,b,c,c,d} and Q={ a,a,b,c,d,e,f,f} then P U Q is 
465A. {a,a,a,a,a,b,b,b,c,c,c,d,d,,e,f,f}
466B. {a,a,b,c,d,e,f}
467C. {a,b,c}
468D. {a,a,a,b,b,c,c,d,e,f,f}
469Answer: D
470
471Let S={1, 2, 3}. How many subsets does S contain?
472A. 3
473B.  6
474C. 8
475D. 4
476Answer: C
477
478
479The number of elements in the power set P(S) of the set S={{Ф},1,{1,2,3} is
480A. 2
481B.  4
482C. 8
483D. NONE
484Answer: C
485
486If A and B are any two sets, then A ∩ (A ∪ B) is equal to
487
488A. B
489B.  AUB
490C. BUA
491D. A
492Answer: A
493
494[~ q ^ (p→q)]→~ p is
495
496A.Satisfiable
497B. tautology
498C. unsatisfiable
499D.  contradiction
500ANSWER : B
501
502The statement ( p^q) → p is a
503
504A.contadiction
505B. tautology
506C. Satisfiable
507D. Contingency
508ANSWER : B
509
510Let p be “He is tall” and let q “He is handsome”. Then the statement “It is false that he is short or handsome is: 
511A.  p ^ q
512B.  ~ (~ p ^q)
513C.  p^ ~ q
514D.  ~ p ^q
515ANSWER : B
516
517
5181. A __________ is an ordered collection of objects.
519a) Relation
520b) Function
521c) Set
522d) Proposition
523Answer: c
524
5252. The set O of odd positive integers less than 10 can be expressed by _____________
526a) {1, 2, 3}
527b) {1, 3, 5, 7, 9}
528c) {1, 2, 5, 9}
529d) {1, 5, 7, 9, 11}
530Answer: b
531
5323. Power set of empty set has exactly _________ subset.
533a) One
534b) Two
535c) Zero
536d) Three
537Answer: a
5384. What is the Cartesian product of A = {1, 2} and B = {a, b}?
539a) {(1, a), (1, b), (2, a), (b, b)}
540b) {(1, 1), (2, 2), (a, a), (b, b)}
541c) {(1, a), (2, a), (1, b), (2, b)}
542d) {(1, 1), (a, a), (2, a), (1, b)}
543Answer: c
544
5455. The Cartesian Product B x A is equal to the Cartesian product A x B. Is it True or False?
546a) True
547b) False
548Answer: b
5496. What is the cardinality of the set of odd positive integers less than 10?
550a) 10
551b) 5
552c) 3
553d) 20
554Answer: b
555
5567. Which of the following two sets are equal?
557a) A = {1, 2} and B = {1}
558b) A = {1, 2} and B = {1, 2, 3}
559c) A = {1, 2, 3} and B = {2, 1, 3}
560d) A = {1, 2, 4} and B = {1, 2, 3}
561Answer: c
562
5638. The set of positive integers is _____________
564a) Infinite
565b) Finite
566c) Subset
567d) Empty
568Answer: a
569
5709. What is the Cardinality of the Power set of the set {0, 1, 2}.
571a) 8
572b) 6
573c) 7
574d) 9
575Answer: a
576
57710. The members of the set S = {x | x is the square of an integer and x < 100} is ________________
578a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
579b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
580c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
581d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}
582Answer: b
58311. The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________
584a) {1, 2, 6, 1}
585b) {1, 2, 5, 6}
586c) {1, 2, 1, 2}
587d) {1, 5, 6, 3}
588Answer: b
589
59012. The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____________
591a) {1, 2}
592b) {5, 6}
593c) {2, 5}
594d) {1, 6}
595Answer: a
596
59713. Two sets are called disjoint if there _____________ is the empty set.
598a) Union
599b) Difference
600c) Intersection
601d) Complement
602Answer: c
603
60414. Which of the following two sets are disjoint?
605a) {1, 3, 5} and {1, 3, 6}
606b) {1, 2, 3} and {1, 2, 3}
607c) {1, 3, 5} and {2, 3, 4}
608d) {1, 3, 5} and {2, 4, 6}
609Answer: d
610
61115. The difference of {1, 2, 3} and {1, 2, 5} is the set ____________
612a) {1}
613b) {5}
614c) {3}
615d) {2}
616Answer: c
617
61816. The complement of the set A is _____________
619a) A – B
620b) U – A
621c) A – U
622d) B – A
623Answer: b
624
62517. The bit string for the set {2, 4, 6, 8, 10} (with universal set of natural numbers less than or equal to 10) is ____________________
626a) 0101010101
627b) 1010101010
628c) 1010010101
629d) 0010010101
630Answer: a
631
63218. Let Ai = {i, i+1, i+2, …..}. Then set {n, n+1, n+2, n+3, …..} is the _________ of the set Ai.
633a) Union
634b) Intersection
635c) Set Difference
636d) Disjoint
637Answer: b
638
63919. The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ___________
640a) 1010100000
641b) 1010101101
642c) 1111111100
643d) 1111101010
644Answer: d
645
64620. The set difference of the set A with null set is __________
647a) A
648b) null
649c) U
650d) B
651Answer: a
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672UNIT 2
673
674
675Sr No	Question	Option 1	Option 2	Option 3	Option 4	Correct Option
6761	The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is	Reflexive 	Transitive	Symmetric	Asymmetric	Transitive
6772	A partial order relation is reflexive, antisymmetric and 	Transitive	Symmetric	Bisymmetric.	Asymmetric	Transitive
6783	The number of functions from an m element set to an n element set is:	mn 	m + n                 	nm 	m  * n	mn 
6794	Let L be a lattice. Then for every a and b in L which one of the following is correct?	a Ú b = a Ù b	a Ú (B Ú C) = (a Ú B) Ú C	a Ú (b Ù c) = a                   	a Ú (b Ú c) = b	a Ú (B Ú C) = (a Ú B) Ú C
6805	A Lattice is called complete, if every non-empty subset has	LUB	GLB	both LUB & GLB	None of these	both LUB & GLB
6816	In a group of 1000 students on campus, at least how many of them must have the same birthDay.                   	5	3	6	4	3
6827	In a group of 29 persons at least how many persons must have born on the same day of the Week.             	5	6	7	8	5
6838	At least how many months of the year must begin on the same day of the week?	2	5	6	4	2
6849	The first 4 terms of the recurrence relation  ak = 2ak-1+k, a1=1, k >= 2, are respectively	1, 4, 11, 26	1, 4, 10, 26              	4,10,26,28         	None of these	1, 4, 11, 26
68510	Let A= {1, 2, 3} B= {2, 4, 5} then number of relations from A to B is	2^6	2^9	2^5	2^3	2^9
68611	For the POSET ({{1},{2},{4},{1,2},{1,4},{2,4},{3,4},{1,3,4},{2,3,4}},⊆) then  The LUB of {{2},{4}} if it exists	{2,3,4}        	{4}                              	{4}            	{2,4}	{2,4}
68712	Let A={1,2,3,4} & R={(1,2),(2,3),(3,4),(2,1)} then the transitive closure of R is	{(1,1), (1,2),(1,3), (1,4) (2,1),(2,2),(2,3) ,(2,4),(3,4)}	{(1,2),(1,3),(1,4) (2,1),(2,2),(2,3)}	{(1,1),(1,3),(2,4), (3,2)}	None of these	{(1,1), (1,2),(1,3), (1,4) (2,1),(2,2),(2,3) ,(2,4),(3,4)}
68813	IF A = {1,2}, B = {5}, then A*B is 	{(1,5),(2,5)}	{(1,1),(1,5)}	{(2,5),(2,2)}	{(5,1),(5,2)}	{(1,5),(2,5)}
68914	IF A = {3,7}, then A^2 is 	{(3,3)}	{(3,3),(3,7),(7,3),(7,7)}	{(3,7),(7,3)}	{(3,3),(7,7)}	{(3,3),(3,7),(7,3),(7,7)}
69015	IF A = {2,3}, B={3,4,5,6} and R is relation from A to B defined as (a,b) belongs to R if a divides b then R is equal to	{(2,4),(2,6),(3,3),(3,6)}	{(6,2),(6,4),(6,3)}	{(3,6),(2,6)}	{(2,2),(3,3)}	{(2,4),(2,6),(3,3),(3,6)}
69116	IF A={3, 4,5} and R is a relation as a<b then R equals to	{(3,4),(3,5)}	{(4,3),(4,5)}	{(3,4),(3,5),(4,5)}	{(3,4),(3,5),(4,5),(4,4)}	{(3,4),(3,5),(4,5)}
69217	IF R={(1,a),(3,a),(3,c)} then inverse of R is 	{(3,a)}	{(b,1),(c,4)}	{(a,1),(a,3),(c,3)}	{(3,a),(4,a)}	{(a,1),(a,3),(c,3)}
69318	If R is a relation on set A and IF (a,a) belongs to R then R is	Reflexive 	antisymetric	Symmetric	transitive	Reflexive 
69419	If R is a relation on set A and IF (a,b) -> (b,a) belongs to R then R is	Reflexive 	antisymetric	Symmetric	transitive	Symmetric
69520	If R is a relation on set A and IF (a,b) (b,c) -> (a,c) belongs to R then R is	Reflexive 	antisymetric	Symmetric	transitive	transitive
69621	If R is a relation on set A and IF (a,b), (b,a) -> a=b belongs to R then R is	Reflexive 	antisymetric	Symmetric	transitive	antisymetric
69722	IF (a,≤) is a poset then subset of a is related to	chain	antichain	hasse diagram	None of these	chain
69823	IF (a,≤) is a poset then subset of a in which no two distinct element are related	chain	antichain	hasse diagram	None of these	antichain
69924	IF R = {(1,1),(1,2),(2,1),(2,2),(3,3)} an equivalence class of two is	{1}	{1,2}	{3}	{1,2,3}	{1,2}
70025	IF R = {(5,5),(6,6),(7,7),(7,8),(8,7),(8,8)} an equivalence class of seven is	{7}	{8}	{5,6}	{7,8}	{7,8}
70126	IF R = {(1,2),(2,3),(3,4)} then transitive closure of R	{(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}	{(1,2),(2,3),(3,4),(1,3)}	{(1,2),(3,4),(4,3)}	{(1,2),(2,3),(3,4),(1,3),(2,4)}	{(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}
70227	The binary relation s = {} on set a = {1,2,3}	Neither reflexive nor symmetric	Symmetric and reflexive	Transitive and reflexive	Transitive and symmetric	Neither reflexive nor symmetric
70328	A relation on a set a is said to be equivalence relation, if it is	Reflexive	Symmetric	Transitive	All of the above	All of the above
70429	A relation r is defined on the set of positive integers as xry if 2x + y ≤ 5.the realation r is	Reflexive	Symmetric	Transitive	None of these	None of these
70530	a relation r is defined on the set of integers as xry if (x + y) is even. Which of the following statements is true?	R is not an equivalence relation	R is an equivalence relation having one equivalence class	R is an equivalence relation having two equivalence classes	R is an equivalence relation having three equivalence classes	R is an equivalence relation having one equivalence class
70631	The number of binary relations on a set with n elements is	N^2	2^N^2	2^n	None of these	2^n
70732	The number of equivalence relations of the set (1, 2, 3, 4) is	4	15	16	24	16
70833	The number of functions from an m element set to an n element set is	m+n	m^n	N^m	m*n	m+n
70934	If a is a finite set with n elements, then number of elements in the largest equivalence relation of a is	1	N	N+1	N^2	N^2
71035	A set of ordered pairs	Coordinates	Domain	Range	Relation	Relation
71136	Find the domain of {(1,2),(2,3),(3,5),(4,5),(5,6)}. Is it a function?	{2,3,5,6}, no	{1,2,3,4,5}, no	{2,3,5,6}, yes	{1,2,3,4,5}, yes	{2,3,5,6}, yes
71237	Which relation is not a function?	{(2,5), (3,6), (4,7), (5,8)}	{(6,-2), (-4,6), (-2,4), (1,0)}	{(-1, 5), (-2,5), (-3,5), (-4,5)}	{(0,-2), (1,0), (-1,-3), (0,-1)}	{(0,-2), (1,0), (-1,-3), (0,-1)}
71338	Let r = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set a = {3, 6, 9, 12}	Reflexive and transitive only	Reflexive only	An equivalence relation	Reflexive and symmetric only	Reflexive and symmetric only
71439	Pigeonhole principle states that a b and |a| >|b| then:	F is not onto	F is not one-one	F is neither one-one nor onto	F may be one-one	F is not one-one
71540	A relation on set a is	An element of a	Subset of a	An element of a*a	Subset of a*a	An element of a*a
71641	Which of the following is the inverse of {(1,2),(2,3),(3,4)}	{(3,4),(2,3),(1,2)}	{(-1,-2),(-2,-3),(-3,-4)}	 {(-3,-4),(-2,-3),(-1,-2)}	{(2,1),(3,2),(4,3)}	{(2,1),(3,2),(4,3)}
71742	Which of the following is the inverse of {(x,y)| x+2y=3}	{(x,y)| 2y+x=3}	 {(x,y)| y+2x=3}	{(x,y)| -x-2y=-3}	{(x,y)| y+2x=3}	{(x,y)| y+2x=3}
71843	Let r be the relation in the set of real numbers defined as R= {(x,y)|1 + ab > 0} is	Reflexive and transitive	Symmetric and transitive	Reflexive and transitive	Equivalence relation	Symmetric and transitive
71944	Let the function f(x) = 5x^2 + 2 then f is	Onto function	One-one & onto function	One-one function	Many-one, into function	One-one & onto function
72045	A relation r in human beings as R= {(x,y)|x loves y} is	Reflexive	Symmetric and transitive	Reflexive and transitive	Equivalence relation	Reflexive
72146	If R is a relation on set A and IF (a,a) belongs to R then R is	Reflexive 	antisymetric	Symmetric	transitive	Reflexive 
72247	IF f(x) = x+2 and g(x) = x-2 then gof is 	x-2	x+2	x	x+1	x
72348	If R is a relation on set A and IF (a,b) (b,c) -> (a,c) belongs to R then R is	Reflexive 	antisymetric	Symmetric	transitive	transitive
72449	IF f(x) = 2x+3 and g(x) = 3x+4 then fog is 	5x+4	7x+5	9x+11	6x+11	6x+11
72550	For the recurrence relation ar-ar-1-6ar-2=0, then the roots are	(2,3)	(3,1)	(1,0)	(-2,3)	(-2,3)
72651	Let M = {1, 2, 3}, and let the relation R in M be the set of points displayed in the coordinate diagram of M × M. Which one of the following statements is true?	a) 1 R 1	b) 3 R 2	c) 2 R 2	d) 2 R 1 	d) 2 R 1 
72752	The relation R is given by the set of ordered pairs, R = {(2, 4), (3, 4), (1,3), (3, 5), (2, 3) }. Which of the following is the domain of R?	a) {2, 3, 1, 5}	b) {1, 2, 3}	c) {1, 2, 3, 4, 5}	d) {2, 4, 3, 5}	b) {1, 2, 3}
72853	Let R be the relation as in Q 3, R = {(2, 4), (3, 4), (1,3), (3, 5), (2, 3)} . What should the range of R be?	a) {3, 4, 5}	b) {1, 2, 3}	c) {1, 2, 3, 4, 5}	d) {4, 4, 2, 5}	a) {3, 4, 5}
72954	Find the inverse of the relation R = {(2, 4), (3, 4), (1,3), (3, 5), (2, 3)} .	a) {(2, 4), (3, 4), (1, 3), (3, 5), (2, 3)}	b) {(4, 2), (4, 3), (3, 1), (5, 3), (3, 2)}	c) {5, 4, 3, 2, 1}	d) {(4, 4), (3, 3), (1, 1), (5, 5), (2, 2)}	b) {(4, 2), (4, 3), (3, 1), (5, 3), (3, 2)}
73055	Which one of the following open sentences defines a reflexive relation on the set of natural numbers?	a) "x is less than y"	b) "x = 2y"	c) "x - y = 5"	d) "x divides y"	d) "x divides y"
73156	. Find the reflexive relation on the set A if A = {a, b, c} .	a) R1 = {(a, b), (b, c), (a, a), (c, c)}	b) R2 = {(a, a), (b, c), (c, c)}	c) R3 = {(a, a), (a, c), (c, a), (b, b), (c, c)}	d) R4 = {(a, a), (c, c), (a, c), (c, a)}	c) R3 = {(a, a), (a, c), (c, a), (b, b), (c, c)}
73257	Which one of the following open sentences defines a symmetric relation in the set of natural numbers N?	a) "x is less than y"	b) "xy = 12"	c) "x - y = 5"	d) "x divides y"	b) "xy = 12"
73358	Find non-symetric relation on the set B = {c, d, e}.	a) R1 = {(e, e)}	b) R2 = {(e, e),(c, d), (d, c)}	c) R3 = B x B	d)R4 = {(c, d), (d, d), (d, e)}	d)R4 = {(c, d), (d, d), (d, e)}
73459	Find the anti-symmetric relation on the set B = {1, 2, 3}.	a) R1 = {(3, 3)}	b) R2 = {(1, 2), (1, 1), (1, 3), (2, 1)}	c) R3 = B × B	d) R4 = {(1, 2), (2, 2), (2, 3), (3, 2)}	a) R1 = {(3, 3)}
73560	Let C = {1, 2, 3, 4}and let R1, R2, R3, R4 be the relations in C. Which one of them is transitive?	a) R1 = {(2, 3), (3, 2), (3, 3), (1, 1)}	b) R2 = {(1, 1), (2, 2), (1, 3), (3, 2)}	c) R3 = {(3, 4), (3, 3), (4, 4), (4, 3)}	d) R4 = {(1, 2), (2, 2), (2, 3), (3, 2)}	c) R3 = {(3, 4), (3, 3), (4, 4), (4, 3)}
73661	Find the transitive relation in the set D = {1, 2, 3, 4}.	a) R1 = {(1, 2), (4, 3), (3, 2), (2, 4)}	b) R2 = {(1, 4), (4, 2), (1, 1), (3, 2)}	c) R3 = {(3, 2), (2, 4), (4, 4), (4, 3)}	d) R4 = {(3, 1), (2, 4), (4, 3), (3, 4)}	d) R4 = {(3, 1), (2, 4), (4, 3), (3, 4)}
73762	Which of the diagrams defines a function of A = {a, b, c, d} into B = {1, 2, 3}	a)	b)	c)	d)	b
73863	Let f 1, f 2, f 3, f 4, f 5 be functions of R into R and let f 1(x) = x2 + 3x - 4. Which of these functions are equal to f 1?	a) f2(x) = x2	b) f3(y) = y2 - 4	c) f4(z) = z2 + 3z - 4	d) f5(x) = x2 + 3x	c) f4(z) = z2 + 3z - 4
73964	The negation symbol is denoted by______.	a. 	b. →	c. ↔	d. v	a. 
74065	P           P is a _____.	a. contradiction.	b. tautology.	c. conditional.	d. biconditional.	a. contradiction.
74166	If there are n distinct components in a statement then there is_________ combinations of values in the truth table.	a. n+1.	b. n2.	c. 2n.	d. n+2.	c. 2n.
74267	If P then Q is called _________ statement.	a. conjunction.	b. disjunction.	c. conditional.	d. biconditional.	c. conditional.
74368	(p→q)→(^q) is __________.	a. tautology .	b. contradiction .	c. WFF.	d. not a WFF.	d. not a WFF.
74469	A relation R in a set X is symmetric if ________.	a. yRx.	b. xRy, yRx.	c. xRy, yRz => xRz.	d. xRy => yRx.	d. xRy => yRx.
74570	. If a relation is reflexive, then all the diagonal entries must be ________.	a. 0.	b. 1.	c. 2.	d. -1.	b. 1.
74671	If R is reflexive, symmetric and transitive then a relation is said to be ________.	a. binary relation.	b. compatibility relation.	c. equivalence relation.	d. partial order relation.	c. equivalence relation.
74772	The set of all finite words over E is denoted by ________.	a. E.	b. E+.	c. E*.	d. λ.	b. E+.
74873	Surjective function is also called ________.	a. one-one.	b. one to one.	c. into.	d. onto.	d. onto.
74974	One to one onto function is also called __________.	a. bijective.	b. injective.	c. surjective.	d. composition function.	a. bijective.
75075	(gof)-1 =________.	a. g-1 .	b. f-1 .	c. g-1 o f-1.	d. f-1 o g-1.	d. f-1 o g-1.
75176	The composition of function is associative but not _______.	a. idempotent.	b. commutative.	c. distributive.	d. de-morgan’s.	b. commutative.
75277	. A mapping x into itself is called __________.	a. relation.	b. equivalence relation.	c. reflexive.	d. transformation.	c. reflexive.
75378	. Which one of the following is Idempotent law?	a. PVF             P.	b. P^T             P.	c. P^P              P.	d. P^F              F.	c. P^P              P.
75479	The duality law of (P^Q)vT is ________.	a. (P^Q)^T.	b. (PvQ)^T .	c. (PvQ)vF .	d. (PvQ)^F.	d. (PvQ)^F.
75580	A product of the variables and their negations in a formula is called _________.	a. elementary product.	b. elementary sum.	c. DNF.	d. CNF.	a. elementary product.
75681	If R = {(1, y), (1, z), (3, y)} then R-1 = ___________.	a. {(1, a), (y, z)}.	b. {(y, z), (z, a), (y, c)}.	c. {(y, a), (1, z), (3, y)}.	d. {(y, a), (z, a), (3, y)}.	b. {(y, z), (z, a), (y, c)}.
75782	Let R ={ (a,b),(c,d),(b,b)}, S = {(d,b),(c,b),(a,d)} then R ° S = ___________.	a. {(a,e),(c,b),(b,e)}.	b. {(d,b),(c,b),(a,d)}.	c. {(a,b),(b,b)}.	d. {(c,b)}.	a. {(a,e),(c,b),(b,e)}.
75883	Let R and s be two relations on a set of positive integers I & R = {(a, 3a+a) / a Є I},S = {(a,a+a)/ a Є I} then R ° R ° R = __________.	a. {(a,3a+a)/ a Є I}.	b. {(a,9a+a)/ a Є I}.	c. {(a,27a+a)/ a Є I}.	d. {(a,9a+c)/ a Є I}.	c. {(a,27a+a)/ a Є I}.
75984	The number of relations from A = {a,b,c} to B = {1,2} are __________.	a. 6.	b. 23.	c. 25.	d. 26.	d. 26.
76085	(A X B)         (A X C) = ___________.	a. A X (B         C).	b. A X (B       C).	c. A X B X C.	d. A         (B X C).	b. A X (B       C).
76186	The minimum number of edges in a connected graph with n vertices is ___________.	a. n-1.	b. n.	c. n+1.	d. n2.	a. n-1.
76287	A graph is planar if and only if does not contain ________.	a. subgraphs homeomorphic to k3 & k3,3.	b. subgraphs isomorphic to k5 or k3,3.	c. subgraphs isomorphic to k3 & k3,3.	d. subgraphs homeomorphic to k5 or k3,3.	d. subgraphs homeomorphic to k5 or k3,3.
76388	Maximum number of edges in an n-node undirected graph without self loops is ____.	a. n 2.	b. [n(n-a.]/2.	c. n-1.	d. [n(n+a.]/2.	b. [n(n-a.]/2.
76489	In any undirected graph the sum of degrees of all the vertices ________.	a. must be even.	b. is twice the number of edges.	c. must be odd.	d. can be even or odd.	d. can be even or odd.
76590	The total number of edges in a complete graph of n vertices is _________.	a. n.	b. n/2.	c. n2-1.	d. [n(n-1]/2.	d. [n(n-1]/2.
76691	A directed complete graph of n vertices contains __________.	a. one arrow between each pair of distinct vertices.	b. two arrows between each pair of distinct vertices.	c. n-1 arrows between each pair of distinct vertices.	d. path between every two distinct vertices.	a. one arrow between each pair of distinct vertices.
76792	A directed graph G = (V, E) is said to be finite if its ________.	a. set V of vertices is finite.	b. set V of vertices & set E of edges are finite.	c. set E of edges are finite.	d. no vertices & edges are repeated.	b. set V of vertices & set E of edges are finite.
76893	Let R = {(3, 3), (6, 6), (9, 9), (1,2), (1,6), (6, 1), (3, 9), (3, 1), (3, 6)} be a relation onthe set A = {3, 6, 9, 12}. The relation is _________	a. reflexive and transitive.	b. reflexive.	c. an equivalence relation.	d. reflexive and symmetric.	a. reflexive and transitive.
76994	A state from which a deterministic finite state automaton can never come out is called a _______	a. transition table.	b. transition diagram.	c. trape state.	d. starting symbol.	c. trape state.
77095	If a compound statement is made up of three simple statements then the number of rows in the truth table is _______.	a. 2.	b. 4.	c. 6.	d. 8.	d. 8.
77196	The conditional statement P→Q is equivalent to _____.	a. Pv Q.	b.       Pv     Q	c. Pv        Q	d. P ΛQ.	b.       Pv     Q
77297	Let R={(1,b.,(3,d.,(2,b.} and S={(4,b.,(2,5),(3,a.} be a relation then R•S=____.	a. {(1,b.,(3,d.,(2,b.}.	b. {(1,5),(3,b.,(2,5)}.	c. {(4,b.,(2,5),(3,a.}.	d. {(1,d.,(3,b.,(2,c.}.	b. {(1,5),(3,b.,(2,5)}.
77398	Let R={(1, 3), (4, 2), (2, 2), (3, 3), (1, 1),(4,4)} be a relation on the set A={1, 2, 3, 4}.The relation R is ________.	a. a function.	b. reflexive.	c. not symmetric.	d. transitive.	c. not symmetric.
77499	The statement p → (q → p) is equivalent to ________.	a. p → (p → q).	b. p→ (p ∨ q).	c. p→ (p ∧ q).	d. p → (p ↔ q).	b. p→ (p ∨ q).
775100	If a relation is reflexive then in the graph of a relation there must be a loop at _____.	a. two nodes.	b. only one nodes.	c. three nodes.	d. each node.	d. each node.
776101	An undirected graph is tripartite if and only if it has no circuits of _______ lengths.	a. odd.	b. even.	c. distinct.	d. equal.	a. odd.
777102	A graph is bipartite if and only if its chromatic number is ________.	a. 1.	b. 2.	c. even.	d. odd.	b. 2.
778103	G is strongly connected implies _________.	a. G is unilaterally connected.	b. G is bilaterally connected.	c. G is unilaterally connected.	d. G has more than one component.	a. G is unilaterally connected.
779104	For a symmetric digraph, the adjacency matrix is _________.	a. symmetric.	b. asymmetric.	c. antisymmetric.	d. symmetric or antisymmetric.	a. symmetric.
780105	The total number of degrees of an isolated node is _______.	a. 0.	b. 1.	c. odd.	d. even.	a. 0.
781106	If G is a connected planar graph then it has a vertex of degree _______.	a. 3 or less.	b. 4 or less.	c. 5 or less.	d. 6 or less.	c. 5 or less.
782107	The less than relation < on real is __________.	a. a partial ordering since it is asymmetric and reflexive.	b. a partial ordering since it is anti-symmetric and reflexive.	c. not a partial ordering since it is not asymmetric and not reflexive.	d. not a partial ordering since it is not anti-symmetric and not reflexive.	d. not a partial ordering since it is not anti-symmetric and not reflexive.
783108	A minimal non-empty edge –cut of G is called a _________.	a. bond.	b. cycle.	c. path.	d. tour.	a. bond.
784109	A connected graph that has no cut vertices is called a ________.	a. bond.	b. block.	c. path.	d. tour.	b. block.
785110	When each element of A is an element of B and each element of B is an element of A, the sets are known as _________.	a. subsets.	b. properties of subsets.	c. equal sets.	d. universal sets.	c. equal sets.
786111	If two sets contain the same distinct elements then it is __________.	a. singleton set .	b. equal set.	c. universal set.	d. none.	b. equal set.
787112	A={1,6,3}, B={2,3,5}, A∩B = ____________.	a. {1,2}.	b. {3}.	c. {6,5}.	d. {6,2}.	c. {6,5}.
788113	If A={0,1,2,3,4,5,6}, B={0,2,4,6,8} then A∩B is ____________ .	a. {0,2,4,6}.	b. {1,2,4,6}.	c. {4,6,8}.	d. {3,4,8}.	a. {0,2,4,6}.
789114	If A= {0,1,2,3,4,5,6}, B={0,2,4,6} and C={0,3,6,9}, A∩B∩C = _________.	a. {0,1,2,3,4,5,6,9}.	b. {0,6}.	c. {0}.	d. {1}.	b. {0,6}.
790115	n(A∪B) is __________.	a. N .	b. 0.	c. n(A)+n(B)-n(A∩B).	d. none.	c. n(A)+n(B)-n(A∩B).
791116	If A= {2, 7, 3}, B= {4, 5}, AUB= __________.	a. {7}.	b. {3, 4, 5}.	c. {2, 7, 3, 4, 5}.	d. {3}.	c. {2, 7, 3, 4, 5}.
792117	If A={a,b,c,d}, B={a,e,i} and C={b,c,d,e}, AUBUC= _________.	a. 0.	b.{i}.	c.{a,b,c,d,e,i}.	d.{a,e,b}.	c.{a,b,c,d,e,i}.
793118	Two sets which have no common elements is said to be ________.	a. disjoint set.	b. equal set .	c. singleton set.	d. universal set.	a. disjoint set.
794119	Let R={(1,b.,(3,d.,(2,b.} and S={(4,b.,(2,5),(3,a.} be a relation then RοS=____.	a. {(1,b.,(3,d.,(2,b.}.	b. {(1,5),(3,b.,(2,5)}.	c. {(4,b.,(2,5),(3,a.}.	d. {(1,d.,(3,b.,(2,c.}.	b. {(1,5),(3,b.,(2,5)}.
795120	The binary relation R = {(0, 0), (1, a.} on A = {0, 1, 2, 3, } is _______.	a. reflexive, not symmetric, transitive.	b. not reflexive, symmetric, transitive.	c. reflexive, symmetric, not transitive.	d. reflexive, not symmetric, not transitive.	b. not reflexive, symmetric, transitive.
796121	Define a binary relation R = {(0, a., (1, b., (2, c., (3, b., (2, 0)} on A = {0, 1, 2, 3} The directed graph (including loops) of the transitive closure of this relation has ______.	a. 16 arrows.	b. 12 arrows.	c. 8 arrows.	d. 6 arrows.	a. 16 arrows.
797122	If f(x)= 2x + 3 and g(x)= 4x then fog is ___________.	a. 8x2 + 3.	b. 8x + 3.	c. 8x3 + 3.	d. 8x4 + 3.	b. 8x + 3.
798123	If an edge e is said to join the vertices u and v then the vertices u and v are called __.	a. initial vertices.	b. terminal vertices.	c. ends of e.	d. all the above.	c. ends of e.
799124	Which one of the following is well formed formula?	a. (P→Q) →(٨Q).	b. (P٨Q)→Q.	c. (P٨Q)→Q).	d. ((P٨Q)→Q).	b. (P٨Q)→Q.
800125	Which of the following statement is the negation of the statement, “2 is even and –3 is negative”?	a 2 is even and –3 is not negative.	b. 2 is odd and –3 is not negative.	c. 2 is even or –3 is not negative.	d. 2 is odd or –3 is not negative.	d. 2 is odd or –3 is not negative.
801126	A partial ordered relation is transitive, reflexive and	a antisymmetric. 	b. bisymmetric.	c. antireflexive.	d. asymmetric.	a antisymmetric. 
802127	The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is	a. Reflexive.	 b. Transitive.	c. Symmetric. 	d. Asymmetric.	 b. Transitive.
803128	A partial order relation is reflexive, antisymmetric and	a. Transitive.	 b. Symmetric.	c. Bisymmetric. 	d. Asymmetric.	a. Transitive.
804129	The number of distinct relations on a set of 3 elements is:	a. 8 	b. 9	c. 18 	d. 512	d. 512
805130	 Which one is the contrapositive of q          p ?	a. p         q 	b. ¬p            ¬q	c. ¬q             ¬p 	d. None of these	b. ¬p            ¬q
806131	 A relation that is reflexive, anti-symmetric and transitive is a	a. function 	b. equivalence relation	c. partial order 	d. None of these	c. partial order 
807132	 ------------ is an association between two objects.	a)      Function	b) Relation   	c) Proposition	 d) Quantifiers	b) Relation   
808133	   -------- is defined to be subset of AXB from a set A to.	a)      Relation 	b) Binary Relation 	c) Both a & b 	d) None	c) Both a & b 
809134	Consider X={1,2,3}; Y={8,9}and R ={(1,8),(2,8),(1,9),(3,9)}. The inverse of relation is 	a)       {(8,1),(8,2),(1,9),(9,3)}	b)     {(8,1),(8,2),(9,1),(9,3)}	c)      {(1,8),(8,2),(9,1),(9,3)}	d)     {(8,1),(2,8),(9,1),(9,3)}	b)     {(8,1),(8,2),(9,1),(9,3)}
810135	      Consider X={2,3,6}; Y={8,9}and R ={(2,8),(2,9),(6,9),(3,9)}. The compliment of relation is 	a)      {(2,8),(3,8),(6,9),(6,9)} 	b)      {(2,9),(6,8),(3,8)}	c)      {(3,8),(2,9),(6,9),(3,9)}	d)     {(3,8),(6,8)}	d)     {(3,8),(6,8)}
811136	         Consider A={1,2,3,4} and R={(1,1)(1,2),(1,4),(2,3),(2,4),(3,4)}. The domain of R is 	a)      {1,2,3}	b)      {1,2,3,4}	c)      {2,3,4}	d)     None  	a)      {1,2,3}
812137	         Consider A={1,2,3,4} and R={(1,1)(1,2),(1,4),(2,3),(2,4),(3,4)}. The Range of R is 	a)      {1,2,3}	b)      {1,2,3,4}	c)      {2,3,4}	d)     None  	b)      {1,2,3,4}
813138	     Let N = {1, 2, 3, ….} be ordered by divisibility, which of the following subset is totally ordered, 	a. (2, 6, 24) 	b. (3, 5, 15) 	c. (2, 9, 16) 	d. (4, 15, 30)	a. (2, 6, 24) 
814139	   A relation R is called ---------if for every elements a€A, aRA.	a)      Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	d) Reflexive
815140	      A relation R is called ---------if for every elements a€A, aRA, i.e (a,a)¢R	a) Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	a) Irreflexive
816141	        A relation R is called ---------if for every elements (a,b)€A implies (b,a)€R.	        a) Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	b) Symmetric  
817142	      A relation R is called ---------if for every elements (a,b), implies (b,a)¢R.	       a) Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	c) Asymmetric 
818143	      A relation R is called ---------if for every elements (a,b)€R and (b,a)€R the a=b.	       a) Antisymmetric	b) Symmetric  	c) Asymmetric 	d) Reflexive	       a) Antisymmetric
819144	          A relation R is called ---------if (a,b)€R and (b,c)€R then aRc.	       a) Antisymmetric	b) Symmetric  	c) Asymmetric 	d) Transitive	d) Transitive
820145	     Let A={1,2,3,4} and R ={(1,1),(2,2),(3,3)}. Is Relation is  	a)      Symmetric and Transitive 	b)      Reflexive and Antisymmetric	c)      Symmetric and Asymmetric  	d)     None 	a)      Symmetric and Transitive 
821146	         A Relation R on set A is called equivalence if it is 	a)      Reflexive	b) Transitive  	c) Symmetric 	d) All 	d) All 
822147	      An equivalence class of an element a is denoted with  	a)      [a]	b) (a)	c) {a}	d) None 	a)      [a]
823148	           Let R be a symmetric and transitive relation on set A. Then?	a)      R is reflexive and hence a partial order 	b)      R is reflexive and hence an equivalence relation 	c)      R is not reflexive and hence not an equivalence relation 	d)     None	d)     None
824149	     Find the domain for the relation: {(1,2), (5,3), (3,6),(2,4)}	A) {1,2,3,5}	B) {2,3,4,6}	c. {1,2,3,6}	d.{2,3,5,6}	A) {1,2,3,5}
825150	        Find the range for the relation:{(3,5), (2,5), (2,6),(3,7)}	A) {5,6,7}	B) {2,3}	c. {1,2,3,6}	d.{2,3,5,6}	A) {5,6,7}
826151	       If A and B are two non empty sets then Cartesian product of A and B is -------------	a)      AXB ={(a,b);a,b€A)}	b)      AXB ={(a,b);a,b€B)}	c)      AXB ={(a,b);a€A and b€B) }	d)     AXB ={(a,b);a€B and b€A) }	d)     AXB ={(a,b);a€B and b€A) }
827152	       If A, B and C are non empty sets then AX(BUC) is ------------	a)      ( AXB) U(AXC)	b)      ( AXB) ∩(AXC)	c)      ( AXB) UC	d)     ( AXC) UB	a)      ( AXB) U(AXC)
828153	        If R is relation defined from set A to B then---------	a)      R=AXB	b)     R    AXB	c)      R     BXA 	d)     AXB         R	b)     R    AXB
829154	        If A,B and C are three sets and B         C then-------	a)      AXB=AXC	b)     AXB         AXC	c)      AXC              AXB	d)     None of these	b)     AXB         AXC
830155	     If A,B and C are three sets then(A-B)XC IS -------------	a)      (AXC)-(BXC) 	b)      (AXC)U(BXC) 	c)      (AXC)-(BXC) 	d)     None of these	a)      (AXC)-(BXC) 
831156	   Find the domain of {(1,2),(2,3),(3,5),(4,5),(5,6)}. Is it a function?	A) {1,2,3,4,5}, yes	B) {1,2,3,4,5}, no	C) {2,3,5,6}, yes	D) {2,3,5,6}, no	A) {1,2,3,4,5}, yes
832157	       If R1 is relation from A to B and R2 is relation from B to C then----	a)      MR1. R2= MR1+ MR2	b)      MR1. R2= MR1- MR2	c)      MR1. R2= MR1. MR2	d)     None of these	c)      MR1. R2= MR1. MR2
833158	   If R1 is relation from A to B and R2 is relation from B to C then------	a)      M(R1.R2)-1= MR1. MR2	b)      M(R1.R2)-1= MR1-1 . MR2-1	c)      M(R1.R2)-1= MR2-1. MR1-1	d)     None of these	c)      M(R1.R2)-1= MR2-1. MR1-1
834159	If R1 and R2  are relations from A to B then --------	a)      (R1U R2 )-1   = R1-1U R2-1	b)      (R1U R2 )-1   = R2-1U R1-1	c)      (R1U R2 )-1   = R1-1∩ R2-1	d)     (R1U R2 )-1   = R2-1∩R1-1	d)     (R1U R2 )-1   = R2-1∩R1-1
835160	     If R1 and R2  are relations from A to B then --------	a)      (R1∩ R2 )-1   = R1-1 ∩ R2-1	b)      (R1∩ R2 )-1   = R1-1U R2-1	c)      (R1∩ R2 )-1   = R2-1∩ R1-1	d)     (R1∩ R2 )-1   = R2-1 U R1-1	c)      (R1∩ R2 )-1   = R2-1∩ R1-1
836161	       If R1 and R2  are relations from A to B then R’ is compliment of R then  ------	a.       (R1∩ R2 )   = R1-1 ∩ R2-1	b.      (R1∩ R2 )   = R1-1U R2-1	c.       (R1∩ R2 )   = R2-1∩ R1-1	d.      (R1∩ R2 )   = R2-1 U R1-1	c.       (R1∩ R2 )   = R2-1∩ R1-1
837162	       A partial ordered relation is transitive, reflexive and 	a. Antisymmetric 	b. Bisymmetric 	c. Anti reflexive. 	d. Asymmetric 	a. Antisymmetric 
838163	       if R is set of real numbers and relation (<=(less than or equal to ) is defined on R then ________	a)      R is an equivalence relation	b)      R is Partial order Relation 	c)      R is symmetric but neither reflexive not transitive 	d)     R is antisymmetric but neither reflexive nor transitive  	a)      R is an equivalence relation
839164	  If f is function from set A to set B then which is true ?	a)      A is known as domain set 	b)      A is known as codomain set	c)      A is known as range	d)     None of these	a)      A is known as domain set 
840165	        If  f: A→B is a function and∀ b∈B ∋a∈A if f(a)=b then __________	a)  f is one to one	b)    f is many one	c)    f is onto	d)    f is into 	a)  f is one to one
841166	     which statement is true	a)      every function is relation  	b)      every relation is function	c)      both a & b	d)     none of these	a)      every function is relation  
842167	       which statement is true	a)      relation can be of the type one to many 	b)      function can be of type one to many	c)       both a & b	d)     None of these	a)      relation can be of the type one to many 
843168	     if R is symmetric and transitive then it is called	a)      equivalence relation	b)     tolerance relation	c)      poset	d)     none of these	b)     tolerance relation
844169	       equivalence class of an element is denoted with_____	a)      [ ]	b)      { }	c)      ( )	d)     None of these	a)      [ ]
845170	   If f :A→B is a function and range of f=B then ?	a)      f is one to one	b)      f is one to many	c)      f is many to one	d)     f is onto	d)     f is onto
846171	        if f:A→B is a function and ∀ b∈B ∋a∈A such that f(a)=b alsof(a1)=f(a2)=>a1=a2 then	a)  f is bijective	b)    f is surjective but not injective	c)    f is injective but not surjective	d)    none of these	a)  f is bijective
847172	        if f:A→B is a function and ∀ b∈B ∋a∈A such that f(a)=b alsof(a1)=f(a2)=>a1=a2 then	a)  f is invertible	b)    f is not invertible	c)    f is many to one onto	d)    none of these	a)  f is invertible
848173	     if A={x,y,z} B={a,b,c,d} and f,g,h,s and t are correspondence defined from A to B such that  f={(x,a),(y,b),(z,c)} g={(x,a),(y,b),(z,c),(x,d)} for f and g, which statement is true?	a)      Both f and g are functions from A to B	b)     f is function from A to  but g is not function	c)      f is not function but g is function from A to B	d)     both f and g are not functions	b)     f is function from A to  but g is not function
849174	1        if A={x,y,z} B={a,b,c,d} and f,g,h,s and t are correspondence defined from A to B such that  f={(x,a),(y,b),(z,c)} then for f which statement is  true?	a)      f is one to one	b)     f is one one into	c)      f is many one onto	d)     f is many one into	b)     f is one one into
850175	2          if A={x,y,z} B={a,b,c,d} and f,g,h,s and t are correspondence defined from A to B such that  g={(x,a),(y,a),(z,b)} for  g, which statement is true?	a)      g is one to one	b)     g is into	c)      g is many one into	d)     g is many one 	b)     g is into
851176	1        if f:A→B is a function then f-1    exists if only if _________	a)      f is many to one onto	b)      f is many to one into	c)      f is one to one onto	d)     f is one to one into	c)      f is one to one onto
852177	2        if f: A→B and g:B→C are two functions then composite of f and g is ______	a)      gof: A→C	b)      fog:A→C	c)      gof:C→A 	d)     fog:C→A	a)      gof: A→C
853178	3        if f: A→B and g:C→D are two functions then fog will exist iff ______	a)      D=A	b)      B=C	c)      A=B	d)     C=D	a)      D=A
854179	1        If S={1,3,5,15,30} and aRb iff a|b then chains of S are _________	a)      {1,3,5,15}	b)      {1,3 15,30}	c)      {1,5,15,30}	d)     Both (b) and (c)	d)     Both (b) and (c)
855180	2        A lattice is a poset(A <=) in which every subset {a,b} of A has_______________	a)      A least upper bound	b)      A greatest lower bound	c)      Both a and b	d)     None of these	c)      Both a and b
856181	1           The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is 	Reflexive 	Transitive 	Symmetric 	Asymmetric	Transitive 
857182	2        Find the number of relations from A = {cat, dog, rat} to B = {male , female} 	15	64	6	32	6
858183	3        If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is 	{(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)} 	{(3,3), (3,4), (3,5)} 	{(3,3), (3,5), (5,3), (5,5)} 	{(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}	{(3,3), (3,5), (5,3), (5,5)} 
859184	4            Let R = { ( 3, 3 ) ( 6, 6 ) ( ( 9, 9 ) ( 12, 12 ), ( 6, 12 ) ( 3, 9 ) ( 3, 12 ), ( 3, 6 ) } be a relation on the set A = { 3, 6, 9, 12 }. The relation is 	A.    Reflexive and transitive 	B.  Reflexive only 	C. An equivalence relation	D.  Reflexive and Symmetric only 	A.    Reflexive and transitive 
860185	5        Let R = { ( 1, 3 ), ( 4, 2 ), ( 2, 4 ), ( 2, 3 ), ( 3, 1 ) } be a relation on the set A = { 1, 2, 3,4 }. The relation R is 	A.    a function 	B.  transitive 	C. not symmetric 	D. reflexive 	C. not symmetric 
861186	6        Evaluate f(x) = 3x - 5 for x = 2	A) f(2) = 27	B) f(2) = 1	C) f(2) = 4	D) none of these	B) f(2) = 1
862187	7        Evaluate f(x) = 3x2 –x+ 5 for x = -2	A) f(-2) = 15	B) f(-2) = 19	C) f(-2) = 14	D) f(-2) = 20	B) f(-2) = 19
863188	8        Find the range for f(x) = -x2 + 3, given the domain {-3, 0, 4}	A) {12,-3,19}	B) {-6,3,-13}	C) {9,-3,-5}	D) {-12,-3,19}	A) {12,-3,19}
864189	9        Find the range for g(x) = x2 - 4x, given the domain {-2,1,3}	A) {12, -2, -3}	B) {12,-3,-3}	C) {6, -2, -3}	D) {6, 3, -3}	B) {12,-3,-3}
865190	10    Find the range of the relation f(x) = 2x2, if the domain is {-2, -1, 0, 3, 4}	A) {8,2,0,18,32}	B) {-8, -2, 0,18,32}	C) {-4,-2,0,6,8}	D) None of these	A) {8,2,0,18,32}
866191	11    Find the range of the relation f(x) = 2x2+1, if the domain is {2, 1, 0, -3, 4}	A) {9,3,1,19,33}	B) {-9,3,1,-19,33}	C) {9,3,0,19,32}	D)  {9,2,1,18,33}	A) {9,3,1,19,33}
867192	1        Evaluate g(x) = 2x2 for x = -2	A) g(-2) = 8	B) g(-2) = -8	C) g(-2) = 4	D) none of these	A) g(-2) = 8
868193	2        if A={a,b,c} and R on A is defined by R={(a,b),(b,a),(a,a),(b,b)} then R is ________	a)      Reflexive and symmetric	b)      Antisymmetric and transitive	c)      Reflexive and transitive	d)      Symmetric and transitive	d)      Symmetric and transitive
869194	3          If A={1,2,3,4,5} and r on A is defined by R={(a,b); b-a=1} then ________	a)      R={(1,2),(2,3),(3,4),(4,5)}	b)      R={(2,1),(3,2),(4,3),(5,4)}	c)      R={(1,2),(2,3),(3,4),(4,5), (2,1),(3,2),(4,3),(5,4)}	d)     None of these	a)      R={(1,2),(2,3),(3,4),(4,5)}
870195	4        If A={1,2,3,4,5,6} and R on A is defined by R={(a,b); a-b=2x where x∈N, N is set of natural numbers} then ________	a)      R={(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}	b)     R={(3,1), (4,2), (5,3), (5,1), (6,4), (6,2)}	c)      R={(1,3), (3,1), (1,5), (5,1), (6,4), (4,6), (5,3), (3,5), (2,6), (6,2), (1,1), (2,2), (3,3), (4,4), (5,5), (6,6),}	d)     None of these	b)     R={(3,1), (4,2), (5,3), (5,1), (6,4), (6,2)}
871196	5        If S={(a,b); a,b ∈I } and (a,b) R (c,d) iff a+d=b+c then__________	a)      R is equivalence relation	b)      R is partial order relation	c)      R is reflexive , transitive but not symmetric 	d)     None of these	a)      R is equivalence relation
872197	6         If N is theset of natural numbers and S={(a,b); a,b ∈N } and (a,b) R (c,d) iff ad=bc then__________	a)      R is equivalence relation	b)      R is partial order relation	c)      R is reflexive ,symmetric but not transitive 	d)     None of these	a)      R is equivalence relation
873198	7        If I set of integers and R is a relation defined on set I. R={(a,b); a divides b or a|b} then ____	a)      R is reflexive but not transitive	b)      R is equivalence relation	c)      R is partial order relation	d)     R is reflexive, transitive but not antisymmetric	d)     R is reflexive, transitive but not antisymmetric
874199	8         If A={2,3,5,6,10,15,30}  and aRb iff a|b then minimal elements of A are ______	a)      2	b) 3	c) 5 	d) All	d) All
875200	9         If A={2,3,5,6,10,15,30}  and aRb iff a|b then maximal elements of A are ______	a)  15	b)10	c)30 	d) All	c)30 
876201	10     If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then upper bound of 2 & 3 are ______	a)  6	b)30	c) both (a) & (b) 	d) none of these	c) both (a) & (b) 
877202	11    If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then lower bound of 2 & 3 are ______	a)  3	b) 5	c) 15 	d) all of these	a)  3
878203	12    If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then greatest lower bound of 30 & 45 are ______	a)  15	b)3	c) 5 	d) allof these	a)  15
879204	13    If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then lower bound of 30 & 45 are ______	a)  15	b)3	c) 5 	d) allof these	d) allof these
880205	14    If A={-2,-1,0,1,2} and f: A→R is defined by f(x)=x2  +1 where R is set of real numbers then __________	a)      f is one to one	b)      f is many to one onto	c)      f is many to one into	d)     f is one to one into	c)      f is many to one into
881
882Q.1. A function is said to be ______________, if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f.
883A. One-to-many
884B. One-to-one
885C. Many-to-many
886D. Many-to-one
887ANSWER: B
888Q.2. The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?
889A. True
890B. False
891C. none
892D. none
893ANSWER: A
894Q.3. The value of ?1/2.?5/2? ? is _______________.
895A. 1
896B. 2
897C. 3
898D. 0.5
899ANSWER: A
900Q.4. Which of the following function f: Z X Z ? Z is not onto?
901A. f(a, b) = a + b
902B. f(a, b) = a
903C. f(a, b) = |b|
904D. f(a, b) = a – b
905ANSWER: C
906Q.5. The domain of the function that assign to each pair of integers the maximum of these two integers is _______.
907A. N
908B. Z
909C. Z+
910D. Z+ * Z+
911ANSWER: D
912
913
914Q.6. Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ________
915A. 6x + 9
916B. 6x + 7
917C. 6x + 6
918D. 6x + 8
919ANSWER: A
920Q.7. __________ bytes are required to encode 2000 bits of data,
921A. 1
922B. 2
923C. 3
924D. 8
925ANSWER: B
926Q.8. The inverse of function f(x) = x3 + 2 is __________.
927A. f -1 (y) = (y – 2) 1/2
928B. f -1 (y) = (y – 2) 1/3
929C. f -1 (y) = (y) 1/3 
930D. f -1 (y) = (y – 2)
931ANSWER: B
932Q.9. The function f(x) = x3 is bijection from R to R. Is it True or False?
933A. True
934B. False
935C. none
936D. none
937ANSWER: A
938Q.10. The g -1({0}) for the function g(x)= ?x? is ________.
939A. {x | 0 = x < 1}
940B. {x | 0 < x = 1}
941C. {x | 0 < x < 1}
942D. {x | 0 = x = 1}
943ANSWER: D
944Q.11.A __________ is an ordered collection of objects
945A. Relation
946B. Function
947C. Set
948D. Proposition
949ANSWER: C
950Q.12.The set O of odd positive integers less than 10 can be expressed by _____________
951A. {1, 2, 3}	
952B. {1, 3, 5, 7, 9}
953C. {1, 2, 5, 9}
954D. {1, 5, 7, 9, 11}
955ANSWER: B
956Q.13. Power set of empty set has exactly _________ subset.
957A. 1
958B. 2
959C. 0	
960D. 3
961ANSWER: A
962Q.14. What is the Cartesian product of A = {1, 2} and B = {a, b}?
963A. {(1, a), (1, b), (2, a), (b, b)}
964B. {(1, 1), (2, 2), (a, a), (b, b)}
965C. {(1, a), (2, a), (1, b), (2, b)}
966D. {(1, 1), (a, a), (2, a), (1, b)}
967ANSWER: C
968Q.15. The Cartesian Product B x A is equal to the Cartesian product A x B. Is it True or False?
969A. True	
970B. False
971C. NULL
972D. NULL
973ANSWER: B
974Q.16. What is the cardinality of the set of odd positive integers less than 10?
975A. 10
976B. 5
977C. 3
978D. 20
979ANSWER: B
980Q.17. Which of the following two sets are equal?
981A. A = {1, 2} and B = {1}
982B. A = {1, 2} and B = {1, 2, 3}
983C. A = {1, 2, 3} and B = {2, 1, 3}
984D. A = {1, 2, 4} and B = {1, 2, 3}
985ANSWER: C
986
987Q.18. The set of positive integers is _____________
988A. Infinite
989B. Finite
990C. Subset
991D. Empty
992ANSWER: A
993Q.19. What is the Cardinality of the Power set of the set {0, 1, 2}.
994A. 8
995B. 6
996C. 7
997D. 9
998ANSWER: A
999Q.20. The members of the set S = {x | x is the square of an integer and x < 100} is ________________
1000A. {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
1001B. {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
1002C. {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
1003D. {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}
1004ANSWER: B
1005
1006
1007
1008From 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? 
1009
1010A. 564  
1011B. 645  
1012C.  756
1013D. None of these
1014
1015ANSWER : D
1016
1017
1018Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
1019
1020A. 210 
1021B. 1050  
1022C.  25200
1023D. None of these
1024
1025ANSWER : C
1026
1027A 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? 
1028
1029A. 32 
1030B. 48  
1031C. 64
1032D. None of these
1033
1034ANSWER : C
1035
1036How 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?
1037
1038A. 40 
1039B. 400  
1040C. 5040
1041D. None of these
1042
1043ANSWER : C
1044
1045 In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? 
1046
1047A. 120  
1048B. 720  
1049C. 756
1050D. None of these
1051
1052ANSWER : B
1053
1054In how many ways can the letters of the CHEATER be arranged
1055
1056A. 2520 
1057B. 360 
1058C. 756
1059D. None of these
1060
1061ANSWER : A
1062
1063In how many way the letter of the word "RUMOUR" can be arranged
1064
1065A. 360
1066B. 180 
1067C. 280
1068D. None of these
1069
1070ANSWER : B
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092UNIT 3
1093
10941)   There are 30 people in a group. If all shake hands with one another, how many handshakes are possible? 
1095a. 870
1096b. 435
1097c. 30!
1098d. 29! + 1
1099
11002)   In how many ways can we arrange the word ‘FUZZTONE’ so that all the vowels come together?
1101a. 1440
1102b. 6
1103c. 2160
1104d. 4320
1105
11063)   In Cricket League, in first round every team plays a match with every other team. 9 teams participated in the Cricket league. How many matches were played in the first round? 
1107a. 36
1108b. 72
1109c. 9!
1110d. 9! - 1
1111
11124)   How many combinations are possible while selecting four letters from the word ‘SMOKEJACK’ with the condition that ‘J’ must appear in it? 
1113a. 81
1114b. 8!/2!
1115c. 3!/2!
1116d. 41
1117
11185)   In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?
1119a. 3
1120b. 30
1121c. 64
1122d. 84
1123
11246)   17 students are present in a class. In how many ways, can they be made to stand in 2 circles of 8 and 9 students?
1125a. 17C9 x 9! X 8!
1126b. 17C9 x 8! X 7!
1127c. 8! X 7!
1128d. 17C8 x 8! X 9!
1129
11307)   On a railway line there are 20 stops. A ticket is needed to travel between any 2 stops. How many different tickets would the government need to prepare to cater to all possibilities? 
1131a. 760
1132b. 190
1133c. 380
1134d. 72
1135
11368)   In Daya’s bag there are 3 books of History, 4 books of Science and 2 books of Maths. In how many ways can Daya arrange the books so that all the books of same subject are together?
1137a. 9
1138b. 6
1139c. 8640
1140d. 1728
1141
11429)   A locker in bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed to by Mahesh to try all the combinations? 
1143a. 90 minutes
1144b. 120 minutes
1145c. 60 minutes
1146d. 100 minutes
1147
114810)   Mayur travels from Mumbai to Jammu in 7 different ways. But he is allowed to return to Mumbai by any way except the one he used earlier. In how many ways can he complete his journey?
1149a. 49
1150b. 42
1151c. 48
1152d. 6
1153
115411)   Without repetition, using digits 2, 3, 4, 5, 6, 8 and 0, how many numbers can be made which lie between 500 and 1000?
1155a. 70
1156b. 147
1157c. 60
1158d. 90
115912)   A trekking group is to be formed having 6 members. They are to be selected from 3 girls, 4 boys and 5 teachers. In how many ways can the group be formed so that there are 3 teachers and 3 boys or 2 girls and 4 teachers
1160a. 55
1161b. 90
1162c. 27
1163d. 144
1164
116513)   If  Suraj doesn’t want three vowels together, then in how many, can he arrange letters of the word 'MARKER'?
1166a. 500
1167b. 720
1168c. 240 
1169d. 360
1170
117114)   A bank has 6 digit account number with no repetition of digits within a account number. The first and last digit of the account numbers is fixed to be 4 and 7. How many such account numbers are possible? 
1172a. 10080
1173b. 5040
1174c. 890
1175d. 1680
1176
117715)   In a class, there are 15 students. During a Christmas party all of them shook hands with each other only once. How many handshakes took place in the class?
1178a. 120
1179b. 210
1180c. 105
1181d. 55
1182
118316)   There are 35 people in a group. There are 12 school girls, 10 school boys, 5 senior citizens and 8 babies in the group. The organizer of the group wants to select a school girl or a school boy as leader of the group. In how many ways can he do so?
1184a. 22
1185b. 1/2
1186c. 13
1187d. 35
1188
118917)   There are 8 routes from London to Delhi. And there are 6 routes from Delhi to Tokyo. In how many different ways can Raj travel from London to Tokyo via Delhi?
1190a. 100
1191b. 48
1192c. 24
1193d. 14
1194
119518)   4 members form a group out of total 8 members. 
1196(i) In how many ways it is possible to make the group if two particular members must be included.
1197(ii) In how many ways it is possible to make the group if two particular members must not be included? 
1198a. 15 and 360
1199b. 15 and 15
1200c. 30 and 360
1201d. 360 and 360
1202
120319)   There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible? 
1204a. 180
1205b. 256
1206c. 386
1207d. 435
1208
120920)   A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
1210a. 12/74
1211b. 24/78
1212c. 13/78
1213d. None of these
1214
1215
1216From 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? 
1217
1218A. 564  
1219B. 645  
1220C.  756
1221D. None of these
1222
1223ANSWER : D
1224
1225
1226Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
1227
1228A. 210 
1229B. 1050  
1230C.  25200
1231D. None of these
1232
1233ANSWER : C
1234
1235A 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? 
1236
1237A. 32 
1238B. 48  
1239C. 64
1240D. None of these
1241
1242ANSWER : C
1243
1244How 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?
1245
1246A. 40 
1247B. 400  
1248C. 5040
1249D. None of these
1250
1251ANSWER : C
1252
1253 In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together? 
1254
1255A. 120  
1256B. 720  
1257C. 756
1258D. None of these
1259
1260ANSWER : B
1261
1262In how many ways can the letters of the CHEATER be arranged
1263
1264A. 2520 
1265B. 360 
1266C. 756
1267D. None of these
1268
1269ANSWER : A
1270
1271In how many way the letter of the word "RUMOUR" can be arranged
1272
1273A. 360
1274B. 180 
1275C. 280
1276D. None of these
1277
1278ANSWER : B
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304UNIT 4
1305
1306Sr No	Question	Option 1	Option 2	Option 3	Option 4	Correct Option
13071	Which of the following statement is true:	Every graph is not its own sub graph.	The terminal vertex of a graph are of degree two.	A tree with n vertices has n edges.	A single vertex in graph G is a sub graph of G.	A single vertex in graph G is a sub graph of G.
13082	A graph in which all nodes are of equal degrees is known as:	Multigraph	Regular graph	Complete lattice  	non regular graph	Regular graph
13093	In an undirected graph the number of nodes with odd degree must be	Zero	Odd	Prime	Even	Even
13104	The length of Hamiltonian Path in a connected graph of n vertices is	n-1	n	n+1	n/2	n-1
13115	A graph with one vertex and no edges is	multigraph 	digraph 	isolated graph 	trivial graph	trivial graph
13126	A complete graph of n vertices should have _____ edges.	n-1    	n	n(n-1)/2 	n(n+1)/2	n(n-1)/2 
13137	A Euler graph is one in which	Only two vertices are of odd degree and rests are even	Only two vertices are of even degree and rests are odd	All the vertices are of odd degree	All the vertices are of even degree	All the vertices are of even degree
13148	The maximum degree of any vertex in a simple graph with n vertex is	n-1	n+1	2n-1	n	n-1
13159	The length of Hamiltonian Path in a connected graph of n vertices is	n-1	n	n+1	n/2	n-1
131610	Let G1 & G2 are two graphs as shown 	Both G1 & G2 are Planer Graph	Both G1 & G2 are Non  Planer Graph	G1 is planer graph but G2 is non planer Graph.	 G1 is non planer graph but G2 is planer graph.	 G1 is non planer graph but G2 is planer graph.
131711	For an undirected graph with n vertices and e edges, the sum of the degree of each vertex is equal to	2n                           (b)      (c)                      (d) 	(2n-1)/2                   	2e      	 e2/2	2e      
131812	Suppose v is an isolated vertex in a graph, then the degree of v is:	0	1	2	3	0
131913	In an undirected graph the number of nodes with odd degree must be	0	odd	Prime	Even	odd
132014	Which of the following statement is true:	Every graph is not its own subgraph	The terminal vertex of a graph is of degree two.	A tree with n vertices has n edges.	A single vertex in graph G is a subgraph of G.	A single vertex in graph G is a subgraph of G.
132115	A graph with one vertex and no edges is:	Multigraph	Digraph	Isolated graph	Trivial graph	Isolated graph
132216	A complete graph of n vertices should have ____ edges.	n	n-1	n(n-1)/2 	n(n+1)/2 	n(n-1)/2 
132317	A Euler graph is one in which	Only two vertices are of odd degree and rests are even	 Only two vertices are of even degree and rests are odd	All the vertices are of odd degree	All the vertices are of even degree	Only two vertices are of odd degree and rests are even
132418	The length of Hamiltonian Path in a connected graph of n vertices is	N	N-1	N+1	N/2	N-1
132519	The degree of any vertex of graph is	The number of edges incident with vertex	Number of vertex in a graph	Number of vertices adjacent to that vertex	Number of edges in a graph	Number of vertices adjacent to that vertex
132620	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	None Of These	K Regular Graph
132721	A graph with no edges is known as empty graph. Empty graph is also known as	Trivial graph	Regular graph	Bipartite graph	None of these	None of these
132822	A graph G is called a ..... if it is a connected acyclic graph	Cyclic graph	Regular graph	Tree	Not a graph	Tree
132923	The complete graph K, has... different spanning trees?	nn-2	n*n	nn	 n2	n*n
133024	A spanning tree of a graph is one that includes	All the vertices of the graph	All the edges of the graph	Only the vertices of odd degree	Only the vertices of even degree	All the vertices of the graph
133125	The number of distinct simple graphs with up to three nodes is	9	7	10	15	9
133226	Consider the graph G where V(G)={A,B,C,D} and E(G)=[{A,B},{B,C},{C,D}]. The degree of each vertices A,B,C,D respectively in G are…..	1,2,3,2	1,3,2,2	 1,1,1,1	 1,2,2,3	 1,1,1,1
133327	The minimum number of spanning trees in a connected graph with “n” nodes is	n-1	n/2	2	1	n-1
133428	The Degree sequence of G is	2,2,3,3,4	 0,1,1,2,0	0,0,1,1,2	2,3,4	0,0,1,1,2
133529	Let H be the plane drawing of the planer graph G. The Graph H has	10	11	6	None Of These	None Of These
133630	The Graph G is Best Described as	Multigraph	A Pseudogarph	A Complete Graph	A Simple Graph	A Simple Graph
133731	The graph g is not a regular graph because	Not all edges are of same length	It is a complete graph	It is a complete graph	Not all vertices have the same degree	Not all vertices have the same degree
133832	The Maximum size of a simple graph of order 15 is	105	210	15	10	15
133933	The size of complete bipartite graph K5,4	20	10	9	25	20
134034	The size of a cyclic graph C5 is	25	5	10	15	10
134135	Two Graphs are Isomorphic if	No. of edges in two graphs are equal	No. of vertices in two graphs are equal	Adjacency is maintained	All of the above	All of the above
134236	A tree with n vertices has _____ edges	n	n+1	n-1	n-2	n-1
134337	A binary Tree T has n leaf nodes. The number of nodes of degree 2 in T is:	log n	n	n-1	n+1	n
134438	A spanning tree of a graph is one that includes	All the vertices of the graph	All the edges of the graph	Only the vertices of odd degree	Only the vertices of even degree	All the vertices of the graph
134539	Which of the following statements is false ?	Every tree is a bipartite graph	A tree contains a cycle	A tree with n nodes contains n-1 edges	A tree is a connected graph	A tree with n nodes contains n-1 edges
134640	A complete binary tree of level 5 has how many nodes?	15	25	63	30	25
134741	The maximum number of nodes on level i of a binary tree is	2i-1	 3i-1	 i+1	2i+2	2i+2
134842	What is the postfix form of the following prefix *+ab–cd	ab+cd–*	abc+*–	ab+*cd–	ab+*cd–	ab+cd–*
134943	The maximum path length from the root to a leaf is a tree’s	Degree	Connectivity count	 Depth	Edge count	 Depth
135044	A connected planer graph divides the plane into a number of regions. If the graph has 8 vertices and these are linked by 20 edges, then the number of regions is:	11	13	21	27	21
135145	The nearest neighbor algorithm for solving the Traveling Salesman Problem is	An optimal and inefficient algorithm	An approximate and efficient algorithm	An approximate and inefficient algorithm	An optimal and efficient algorithm	An optimal and efficient algorithm
135246	A tree is	any graph with one component.	any graph that is connected and has no circuits.	any graph that has no bridges.	any graph that has no circuits.	any graph that is connected and has no circuits.
135347	The number of chords of tree of a connected graph G of v vertices and e edges is	v - 1	 e – v + 1	v + 1	e – v -1	 e – v + 1
135448	A graph in which all nodes are of equal degrees is known as:	Multigraph	Regular graph	Complete lattice  	non regular graph	Regular graph
135549	The prefix evolution of (a + b) * (c + d) is:	Ab + cd + *	*+ab +cd	+ab + cd + *	None of these	*+ab +cd
135650	Evaluate the following prefix expression ++ 26 + - 1324	25	12	15	23	15
135751	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 	n(n – 1)/2 
135852	In a graph if e=[u, v], Then u and v are called 	Endpoints of e 	Adjacent nodes 	Neighbors 	All of above 	All of above 
135953	A vertex of a graph is called even or odd depending upon 	Total number of edges in a graph is even or odd	Total number of vertices in a graph is even or odd 	Its degree is even or odd 	None of these 	Its degree is even or odd 
136054	Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to 	15	30	90	360	15
136155	The maximum degree of any vertex in a simple graph with n vertices is 	n–1 	n+1 	2n–1 	n 	n–1 
136256	McCabe’s cyclomatic metric V(G) of a graph G with n vertices, e edges and p connected component is 	e 	n 	e – n + 2p 	e – n + p 	e – n + p 
136357	Which of the following statement is true 	Every graph is not its own subgraph 	The terminal vertex of a graph are of degree two	A tree with n vertices has n edges	A single vertex in graph G is a subgraph of G. 	A single vertex in graph G is a subgraph of G. 
136458	Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex s to u has weight 53 and shortest path from s to v has weight 65. Which statement is always true ? 	Weight (u, v) <= 12 	Weight (u, v) = 12 	Weight (u, v) >= 12 	Weight (u, v) > 12 	Weight (u, v) >= 12 
136559	The minimum number of edges in a connected graph with ‘n’ vertices is equal to	n(n–1) 	n(n–1)/2 	n2 	n–1 	n–1 
136660	Which one of the following statements is incorrect ? 	The number of regions corresponds to the cyclomatic complexity	Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph	Cyclometric complexity for a flow graph G is V(G) = E–N+2, where E is the number of edges & N is the number of nodes in the flow graph. 	Cyclometric complexity for a flow graph G is V(G) = P + 1, where P is the number of predicate nodes contained in the flow graph G. 	Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph
136761	A minimal spanning tree of a graph G is 	A spanning sub graph 	A tree 	Minimum weights	All of above 	All of above 
136862	Which of the following statements is/are TRUE for undirected graphs?  P: Number of odd degree vertices is even    Q: Sum of degrees of all vertices is even
1369	P only 	Q only 	Both P and Q 	Neither P nor Q 	Both P and Q 
137063	In any complete 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 	Are twice the number of edges 
137164	A graph with no edges is known as empty graph. Empty graph is also known as	Trivial graph 	Regular graph 	Bipartite graph 	None of these 	Trivial graph 
137265	The length of Hamiltonian Path in a connected graph of n vertices is 	n–1 	n 	n+1 	n/2 	n–1 
137366	A 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 	greater than n–1 
137467	In a graph if e=(u, v) means 	u is adjacent to v but v is not adjacent to u 	e begins at u and ends at v 	u is processor and v is successor 	both b and c 	both b and c 
137568	The complete graph with four vertices has k edges where k is 	3	4	5	6	6
137669	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 	The number of edges in walk W 
137770	The number of colours required to properly color vertices of every planar graph is 	2	3	4	5	2
137871	Choose the most appropriate definition of plane graph 	A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices 	A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y 	A simple graph which is Isomorphic to Hamiltonian graph 	None of these 	A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices 
137972	Suppose v is an isolated vertex in a graph, then the degree of v is 	0	1	2	3	0
138073	In the planar graph, the graph crossing number is 	0	1	2	3	0
138174	Which of the following graph is not possible? 	Graph with four vertices of degrees 1, 2, 3 and 4	Graph with four vertices of degrees 1, 2, 3 and 5	Graph with three vertices of degrees 1, 2 and 3	Graph with three vertices of degrees 1, 2 and 5	Graph with four vertices of degrees 1, 2, 3 and 4
138275	The minimum number of edges for a graph with seven vertices to be connected is	4	5	6	7	4
138376	
1384coonnected planar graph divides the plane into a number of regions. If the graph
1385A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by 13 edges, then the number of regions is	5	6	7	8	7
138677	Suppose v is an pendant vertex in a graph, then the degree of v is 	0	1	2	3	0
138778	If H is spanning subgraph of graph G such that degree of each vertex of H is K then H is called	K-factor graph of G	null subgraph of g	complement of grapf G	None of these 	K-factor graph of G
138879	If a graph G is isomorphic to its its complement then G is called	complete graph	bipartite graph	self complementory graph	None of these 	self complementory graph
138980	A graph posseses an Eulerion Circuit iff if it is connected and has vertices which all have 	even degrees	old degrees	degree one 	degree three	even degrees
139081	A minimal non-empty edge –cut of G is called a _________.	a. bond.	b. cycle.	c. path.	d. tour.	a. bond.
139182	A connected graph that has no cut vertices is called a ________.	a. bond.	b. block.	c. path.	d. tour.	b. block.
139283	If an edge e is said to join the vertices u and v then the vertices u and v are called __.	a. initial vertices.	b. terminal vertices.	c. ends of e.	d. all the above.	c. ends of e.
139384	Edges intersect only at their ends are called ________.	a. planar.	b. loop.	c. link.	d. non planar.	a. planar.
139485	Two vertices which are incident with the common edge are called __________ as are two edges which are incident with the common vertex.	a. distinct.	b. directed.	c. adjacent.	d. loops.	c. adjacent.
139586	An edge with identical ends is called _________.	a. complete graph.	b. bipartite graph.	c. loops.	d. link.	c. loops.
139687	An edge with the distinct ends is called ___________.	a. complete graph.	b. bipartite graph.	c. loops.	d. link.	d. link.
139788	A simple graph in which each pair of distinct vertices is joined by an edge is called a__________.	a. empty graph.	b. complete graph.	c. simple graph.	d. bipartite graph.	c. simple graph.
139889	The graph is said to be a simple graph if it has _________.	a. no links.	b. no loops.	c. no vertices.	d. no edges.	b. no loops.
139990	Each edge has one end in X and one end in Y then the graph (X, Y) is called _____.	a. simple.	b. empty.	c. complete.	d. bipartite.	d. bipartite.
140091	The graph defined by the vertices and edges of a __________ is bipartite.	a. square.	b. cube.	c. single.	d. both (a) and (b).	b. cube.
140192	Which of the following statements is true?	a. A number is rational if and only if its square is rational.	b. An integer n is odd if and only if n2 + 2n is odd.	c. A number is irrational if and only if its square is irrational.	d. A number n is odd if and only if n(n + a. is even.	b. An integer n is odd if and only if n2 + 2n is odd.
140293	To any graph G there corresponds a v × € matrix is called ________.	a. incidence matrix.	b. adjacency matrix.	c. square matrix.	d. null matrix.	a. incidence matrix.
140394	If H is a sub graph of G then G is a ______ of H.	a. proper sub graph.	b. induced sub graph.	c. spanning sub graph.	d. super graph.	d. super graph.
140495	If the graph G1 and G2 has no vertex in common then it is said to be ______.	a. disjoint.	b. edge disjoint.	c. union .	d. intersection.	a. disjoint.
140596	The degree of vertex v in G is __________.	a. number of edges of G incident with v.	b. number of loops in G.	c. number of links in G.	d. number of sub graph in G.	a. number of edges of G incident with v.
140697	If the edges of a walk Ware distinct then Wis called _________.	a. path.	b. trial.	c. walk.	d. tour.	d. tour.
140798	The number of primes of the form |n2 − 6n + 5| where n is an integer is _____.	a. 0 .	b. 1 .	c. 2 .	d. 3 .	c. 2 .
140899	If the vertices of a walk W are distinct then W is called __________.	a. path.	b. trial.	c. walk.	d. tour.	a. path.
1409100	If a walk has positive length and its origin and terminals are same then it is called ------------	a. open.	b. loop.	c. closed.	d. trial.	c. closed.
1410101	In the following graph                                          the Euler path is	a. abcdef 	b. abcf	c. fdceab  	d. fdeabc	c. fdceab  
1411102	A graph in which all nodes are of equal degrees is known as:	a. Multigraph	b. Regular graph	c. Complete lattice 	d. non regular graph	b. Regular graph
1412103	 Transitivity and irreflexive imply:	a. Symmetric 	b. Reflexive	c. Irreflexive 	d. Asymmetric	d. Asymmetric
1413104	 In an undirected graph the number of nodes with odd degree must be	a. Zero 	b. Odd	c. Prime 	d. Even	d. Even
1414105	 Find the number of relations from A = {cat, dog, rat} to B = {male , female}	a. 64 	b. 6	c. 32 	d. 15	a. 64 
1415106	 The number of functions from an m element set to an n element set is:	a. mn 	b. m + n	c. nm 	d. m * n	a. mn 
1416107	 Which of the following proposition is a tautology?	a. (p v q)          p	 b. p v (q         p)	c. p v (p         q) 	d. p        (p         q)	c. p v (p         q) 
1417108	 A graph with one vertex and no edges is:	a. multigraph 	b. digraph	c. isolated graph 	d. trivial graph	d. trivial graph
1418109	If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is	a. {(3,3), (3,4), (3,5)}	b. {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}	c. {(3,3), (3,5), (5,3), (5,5)}	d. {(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}	c. {(3,3), (3,5), (5,3), (5,5)}
1419110	 A complete graph of n vertices should have __________ edges.	a. n-1 	b. n	c. n(n-1)/2 	d. n(n+1)/2	c. n(n-1)/2 
1420111	 A Euler graph is one in which	a. Only two vertices are of odd degree and rests are even	b. Only two vertices are of even degree and rests are odd	c. All the vertices are of odd degree	d. All the vertices are of even degree	d. All the vertices are of even degree
1421112	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	all of even degree
1422113	A graph is a collection of	Row and columns	Vertices and edges	Equations	None of these	Vertices and edges
1423114	A graph G is called a ..... if it is a connected acyclic graph	Cyclic graph	Regular graph	Tree	Not a graph	Tree
1424115	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	n(n – 1)/2
1425116	In a graph if e=[u, v], Then u and v are called	Endpoints of e	Adjacent nodes	Neighbors	All of above 	All of above 
1426117	In a graph if e=(u, v) means	u is adjacent to v but v is not adjacent to u	e begins at u and ends at v	u is processor and v is successor	both b and c	both b and c
1427118	A vertex of a graph is called even or odd depending upon	Total number of edges in a graph is even or odd	Total number of vertices in a graph is even or odd	Its degree is even or odd	All of above 	Its degree is even or odd
1428119	Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to	15	30	90	360	15
1429120	The maximum degree of any vertex in a simple graph with n vertices is	n–1	n+1	2n–1	n	n–1
1430121	Hasse diagram are drawn	Partially ordered sets	Lattices	Boolean algebra	None of these	Partially ordered sets
1431122	Which of the following statement is true	Every graph is not its own subgraph	The terminal vertex of a graph are of degree two	A tree with n vertices has n edges.	A single vertex in graph G is a subgraph of G	A single vertex in graph G is a subgraph of G
1432123	A connected graph T without any cycles is called	A tree graph	Free tree	A tree	All of above	All of above
1433124	Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex s to u has weight 53 and shortest path from s to v has weight 65. Which statement is always true ?	Weight (u, v) <= 12	Weight (u, v) = 12	Weight (u, v) >= 12	Weight (u, v) > 12	Weight (u, v) >= 12
1434125		Both G1 and G2 are planar graphs	Both G1 and G2 are not planar graphs	G1 is planar and G2 is not planar graph	G1 is not planar and G2 is planar graph.	G1 is not planar and G2 is planar graph.
1435126	The minimum number of edges in a connected graph with ‘n’ vertices is equal to	n(n–1)	n(n–1)/2	n2	n–1	n–1
1436127	Which one of the following statements is incorrect ?	The number of regions corresponds to the cyclomatic complexity.	Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph	Cyclometric complexity for a flow graph G is V(G) = E–N+2, where E is the number of edges & N is the number of nodes in the flow graph.	Cyclometric complexity for a flow graph G is V(G) = P + 1, where P is the number of predicate nodes contained in the flow graph G.	Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph
1437128	A minimal spanning tree of a graph G is	A spanning sub graph	A tree	Minimum weights	All of above	All of above
1438129	Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even.Q: Sum of degrees of all vertices is even.	P only	Q only	Both P and Q	Neither P nor Q	Both P and Q
1439130	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            	Are twice the number of edges.
1440131	The graph g is not a regular graph because	Not all edges are of same length	It is a complete graph	It is a complete graph	Not all vertices have the same degree	Not all vertices have the same degree
1441132	The Maximum size of a simple graph of order 15 is	105	210	15	10	15
1442133	The minimum number of edges for a graph with seven vertices to be connected is	4	5	6	7	6
1443134	Which of the following graphs is a spanning tree for the network shown					
1444135	For the graph shown, which vertex has degree 5?	Q	T	s	R	Q
1445136	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	25
1446137	A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by 13 edges, then the number of regions is:	5	6	7	8	7
1447138	For the graph shown, which of the following paths is a Hamilton circuit?	ABCDCFDEFAEA	AEFDCBA	AFCDEABA	ABCDEA	AEFDCBA
1448139	The sum of the degrees of the vertices on the graph shown here is:	20	21	22	23	22
1449140	For the graph shown, which additional arc could be added to the network so that the graph formed would contain an Euler path?	AF	DE	AB	CF	DE
1450141	For the graph shown here, the minimum length spanning tree has length:	30	31	34	36	30
1451142	Of the following graphs, which one has both Euler and Hamilton circuits?					
1452143	Which one of the following graphs has an Euler circuit?					
1453144	The complete graph with four vertices has k edges where k is 	3	4	5	6	6
1454145	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 	The number of edges in walk W 
1455146	Which one of the following is a spanning tree for the graph shown here?					
1456147	Which one of the following graphs has an Euler circuit?					
1457148	Which one of the following graphs provides a counter-example to the statement: ‘For a graph with seven vertices, if graph contains a Hamilton circuit’?the degree of each vertex is greater than 2 then the					
1458149	For which one of the following graphs is the sum of the degrees of the vertices equal to 20?					
1459150	Which one of the following paths is a Hamilton circuit for the graph shown here?	PQRSTP 	PQRSTUVP 	PQUVRSTP 	PQRSTUVUTP	PQUVRSTP 
1460
1461
1462
1463Q. 1	Graph is collection of
1464(a)	points and plane 		(b)	edges and vertex
1465(c)	edges and weights 		(d)	vertex and plane				Ans. : (b)
1466Q. 2	An edges whose end vertices are same are called
1467(a)	self loop 			(b)	parallel  edges 
1468(c)	circuit			(d)	path									Ans. : (a)
1469Q. 3	If more than one edges are associated with a pair of vertex then it is called
1470(a)	parallel edges		(b)	self loop
1471(c)	circuit				(d)	simple graph						Ans. : (a)
1472Q. 4	A Graph having no parallel edges or self loops are called 
1473(a)	Isolated graph			(b)	Simple graph
1474(c)	Multi graph				(d)	Regular graph					Ans. : (b)
1475Q. 5	A graph containing the self loop or parallel edges are called 
1476(a)	Simple graph 			(b)	Multi graph
1477(c)	Regular graph			(d)	Path							Ans. : (b)
1478Q. 6	The vertex which is not connected to any edges are called 
1479(a)	Isolated vertex 			(b)	Pendant vertex
1480(c)	Adjacent vertex			(d)	None of these					Ans. : (a)
1481Q. 7	A graph in which all the vertices are of equal degree are called
1482(a)	Regular graph 			(b)	Multi graph
1483(c)	Simple graph 			(d)	None of these					Ans. : (a)
1484Q. 8	The total number of edges in a complete graph is. 
1485(a)	n (n  1)		(b)	n/2
1486(c)	(n  1)		(d)	n (n  1)/ 2									Ans. : (d)
1487Q. 9	The maximum number of edges in any graph is 
1488(a)	n (n  1)			(b)	n/2
1489(c)	n (n  1)/ 2		(d)	(n  1)									Ans. : (c)
1490Q. 10	A graph having no edges are called 
1491(a)	Isolated graph 		(b)	Null graph 
1492(c)	Regular graph 		(d)	None 								Ans. : (b)
1493Q. 11	A vertex with degree one is called
1494(a)	Isolated vertex 			(b)	Pendant vertex 
1495(c)	Adjacent vertex 			(d)	Null graph					Ans. : (b)
1496Q. 12	A subgraph which contains all the vertex of a graph is called 
1497(a)	Spanning subgraph		(b)	Complement of a graph 
1498(c)	Subgraph 				(d)	None of these					Ans. : (a)
1499Q. 13	The number of vertices in a bipartite graph Km, n is 
1500(a)	m + n		(b)	m ( n
1501(c)	m			(d)	n											Ans. : (a)
1502Q. 14	Total number of edges in a complete bipartite graph Km, n is 
1503(a)	m + n 		(b)	m * n
1504(c)	m			(d)	n											Ans. : (b)
1505Q. 15	If V1 is one set of vertex and V2 is other set of vertex then in case of bipartite graph V1 ( V2 is,
1506(a)	V		(b)	V1		(c)	V2		(d)	(					Ans. : (d)
1507Q. 16	If V1 is one set of vertex and V2 is other set of vertex then in case of bipartite graph V1 ( V2 is 
1508(a)	V		(b)	V1		(c)	V2		(d)	(					Ans. : (a)
1509Q. 17	If every edge of one set of vertex is connected with every vertex of other set of vertex then the graph is called 
1510(a)	Bipartite graph 			(b)	Complete bipartite graph
1511(c)	Regular graph			(d)	Complete graph				Ans. : (b)
1512.
1513Q. 18	If every vertex of graph is adjacent to the all other remaining vertex of graph then it is called 
1514(a)	Complete graph 			(b)	Regular graph
1515(c)	Bipartite graph 			(d)	None of these					Ans. : (a)
1516Q. 19	Maximum degree of a vertex in a simple graph is 
1517(a)	n 			(b)	(n  1)
1518(c)	n/2			(d)	n (n  1)/ 2									Ans. : (b)
1519Q. 20	How many nodes are necessary to construct a graph with exactly 6 edges in which each node is of degree 2  ______ ?
1520(a)		6		(b)	8		(c)	4		(d)  10						Ans. : (a)
1521Q. 21	What is the number of edges in a graph K10.
1522(a)	40		(b)	45	(c)	50		(d)	48						Ans. : (b)
1523Q. 22	What is the number of edges in a graph Km, n (K5, 7)
1524(a)	30		(b)	32		(c)	35		(d)  40						Ans. : (c)
1525Q. 23	An Isomorphic graph should have
1526(a)	equal number of vertices 		
1527(b)	equal number of edges
1528(c)	equal number of vertices with a given degree
1529(d)	All the above three											Ans. : (d)
1530Q. 24	Whether the graph K6 and K3, 3 are Isomorphic or not ? 
1531(a)	Yes 			(b)	No										Ans. : (b)
1532Explanation : 
1533K6 is a complete graph with n = 6
1534Number of edges = n (n  1)/2 ( 6 (6  1)/ 2 = 15
1535K3, 3 is a bipartite graph with number of vertex = 3 + 3 = 6
1536But the number of edges = m * n = 3 + 3 = 9
1537So, K6 have 15 edges while K3, 3 have 9 edges 
1538So the given graph is not isomorphic.
1539Q. 25	A spanning subgraph with equal degree of all the vertices are called
1540(a)	factor of a graph 				(b)	complement of a graph
1541(c)	vertex disjoint subgraph 		(d)	edge disjoint subgraph	
1542Ans. : (a)
1543
1544Q. 26	The minimum number of edges in a connected cyclic graph of n vertices is 
1545(a)	n  1			(b)	n
1546(c)	n + 1			(d)	None of these							Ans. : (b)
1547Q. 27	The number of distinct simple graph with up to 3 node is 
1548(a)	15		(b)	10		(c)	7		(d)  9						Ans. : (c)
1549Explanation : 	(c)
1550Q. 28	In any undirected graph the sum of degree of all the nodes
1551(a)	must be even			(b)	twice the number of edges
1552(c)	must be odd 			(d)	need not even					Ans. : (b)
1553Q. 29	Number of vertices of odd degree in a graph is
1554(a)	always even 			(b)	always odd
1555(c)	either even or odd 		(d)	200						   		Ans. : (a)
1556Q. 30	Maximum degree of any node in a simple graph with n vertices is 
1557(a)	n  1		(b)	n 	(c)	n/2		(d)	n  2				Ans. : (a)
1558Q. 31		A given connected graph is Euler graph if and only if all vertices of G are of 
1559(a)	same degree 		(b)	even degree 
1560(c)	odd degree			(d)	different degree					Ans. : (b)
1561Q. 32	A graph is a tree if and only if it is 
1562(a)	completely connected 		(b)	minimally connected 
1563(c)	contains circuit 				(d)	is planar					Ans. : (b)
1564Q. 33	 A complete graph with n vertices is 
1565(a)	2-chromatic 			(b)	n/2 chromatic 
1566(c)	(n  1) chromatic 		(d)	n-chromatic 					Ans. : (d)
1567Q. 34	The length of a Hamilton path (if exists) in a connected graph of n vertices is
1568(a)	n  1			(b)	n
1569(c)	n + 1			(d)	n/2										Ans. : (a)
1570Q. 35	T is a graph with n vertices. T is connected and has exactly n  1 edges then
1571(a)	T is a tree 
1572(b)	T contains no cycle
1573(c)	Every pair of vertices in T is connected by exactly one path
1574(d)	Addition of new edge will create a cycle 	 				Ans. : (a)
1575Explanation : 	Theorem
1576Q. 36	A graph can be drawn with 4 edges having vertices of degree.
1577(a)	4, 3, 2, 1			(b)	3, 2, 1, 0
1578(c)	4, 5, 6, 7			(d)	3, 2, 2, 1							Ans. : (d)
1579Q. 37	What would be the minimum number of edges in a connected graph having 11 vertices.
1580(a)	5		(b)	10		(c)	15		(d)  20						Ans. : (b)
1581Q. 38	Which of the statements are false ?
1582(a)	A graph coursing exists for a graph if the graph has no isolated vertex
1583(b)	No minimal coursing can contain a circuit
1584(c)	A Hamilton circuit is a covering
1585(d)	A spanning tree is covering
1586(a) c and d 		(b) b		(b) a and c 	(b)	None			Ans. : (d)
1587Q. 39	Match the list 1 with list II
1588			List I							List II
1589Hamilton path		(i)	Contains minimal covering
1590Every covering 		(ii)	Contains every vertex of the graph only once
1591Non-planar graph 	(iii)	Contain K5 or K3, 3 as sub-graph 
1592(a)	A  3	b  1	c 2				(b)	a  2		b  1    c  3
1593(c)	a  2	b  3	c  1			(d)	None of these		Ans. : (b)
1594Q. 40	The graph QK
1595(a)	has 2K vertices 		(b)	K is regular
1596(c)	Both a and b 		(d)	None of these						Ans. : (c)
1597Q. 41	If G is a planar graph with 35 regions each of degree 6, the number of vertices are,
1598(a)	70		(b)	80		(c)	72		(d)  62						Ans. : (c)
1599				
1600Q. 42	Chromatic number of a tree with n vertices is 
1601(a)	n  1		(b)	n + 1	(c)	2n		(d)	(n/2)	(e)	2		Ans. : (e)
1602
1603
1604Q. 43	
1605
1606G1 			        G2 			                  G3
1607Which of the following is true?
1608G2 and G3 are isomorphic		(b)	G1 and G2 are isomorphic 
1609(c)	G3 is a simple graph 		(d)	G1, G2 and G3 are simple graph 
1610Ans. : (b)
1611Q. 44	Chromatic number of the following graph is
1612(a)	2	(b)	3	(c)	4	(d)	5									Ans. : (b)
1613
1614Fig. Q. 44
1615Q. 45	Kn has perfect matching if n is
1616(a)	odd		(b)	even 	(c)	prime		(d)	( 4				Ans. : (b)
1617Q. 46	Consider the following statement
1618S1 : A planar graph is 5 colourable
1619S2 : Kn is planar if n ( 4
1620(a)	both S1 and S2 are true 		(b)	S1 is true 
1621(c)	S2 is true 					(d)	none						Ans. : (c)
1622Q. 47	The diameter of the following graph is 
1623
1624Fig. Q. 47  
1625(a)	2		(b)	6		(c)	5		(d)  3						Ans. : (d)
1626Q. 48	Consider the graph G1 and G2
1627		
1628G1 				G2
1629Fig. Q. 48
1630	Which of the following is true
1631(a)	G1 has Euler circuit 			(b)	G2 has Euler circuit
1632(c)	Both (a) and (b) are valid		(d)	None				Ans. : (a)
1633Q. 49	If a graph (G) is a connected planar graph with e edge and v vertices where 
1634v ( 3 then
1635(a)	e = 3 v  6			(b)	e ( 3 v  6
1636(c)	e = 3 v + 6			(d)	e ( 3 v + 6							Ans. : (b)
1637
1638
1639Q. 50	The number of perfect matching in a tree with n vertices is 
1640(a)	2			(b)	( 1		(c)	n  1			(d)	
1641Ans:	(b)
1642Q. 51	Determine the chromatic number of the following graph.
1643
1644Fig. Q. 51
1645(a)	2			(b)	3		(c)	4			(d)	5				Ans. : (c)
1646Q. 52	The chromatic number of a star graph with n vertices is 
1647(a)	2		(b)	4			(c)	n  1		(d)	n/2				Ans. : (a)
1648Q. 53	Chromatic number of a complete graph Kn is 
1649(a)	n 		(b)	n/2		(c)	n  1		(d)	n + 1				Ans. : (a)
1650Q. 54	Every bipartite graph have the chromatic number 
1651(a)	n 		(b)	n  1		(c)	2		(d)	n/2					Ans. : (c)
1652Q. 55	Consider the graph G1 and G2
1653
1654G1 			G2
1655Fig. Q. 55
1656	Which of the following is true?
1657(a)	G2 has Euler path 	(b)	G1 has neither Euler circuit nor Euler path
1658(c) Both (a) and (b)		(d)	None of these			Ans. : (c)
1659Q. 56	Consider the graph G1 and G2
1660
1661Fig. Q. 56
1662(a)	G1 has Hamilton circuit			
1663(b)	G2 has Hamilton circuit
1664(c)	Neither G1 nor G2 has Hamilton circuit
1665(d)	Both G1 and G2 have Hamilton circuit 						Ans. : (b)
1666
1667Q. 57	What is the height of the given graph ?
1668
1669
1670
1671Fig. Q. 57
1672(a)		3	(b)	4	(c)	5	(d)  2									Ans. : (b)
1673Q. 58	Compare the two figures and conclude
1674
1675Fig. Q. 58
1676(a)	Isomorphic 		
1677(b)	Not isomorphic as G2 has no vertex with indegree = 2
1678(c)	Not isomorphic as G2 has no vertex with outdegree = 2
1679(d)	both (b) and (c)												Ans. : (d)
1680Q. 59	The minimum number of edges in a connected cycle graph of n vertices is 
1681(a)	n  1		(b)	n	(c)	n + 1	(d)	None				Ans. : (b)
1682Q. 60	The degree of each reason in a polyhedra graph (degree of each region ( 3) with 12 vertices and 30 edges is, 
1683(a)	2		(b)	4		(c)	3		(d)  5						Ans. : (c)
1684					
1685	
1686
1687Q. 61	Find the least number of vertices of a complete graph having at least 50 edges.
1688(a)	25		(b)	20		(c)	15		(d)  10						Ans. : (d)
1689Q. 62	A graph needs a chromatic number n. This can be shown by 
1690(i)	Showing that the graph can be coloured with n colours
1691(ii)	Showing that the graph can not be coloured using < n colours
1692(a)	only (i) 	  (b) only (ii) 		(c) (i) and (ii) 	  (d)  None			Ans. : (c)
1693Q. 63	Find the chromatic number of the given graph.
1694
1695
1696
1697Fig. Q. 63
1698(a)	3	(b)	4		(c)	5	(d)   2								Ans. : (b)
1699Q. 64	Chromatic number of cycle graph Cn, n > 1 and n is odd.
1700(a)	2		(b)	3		(c)	4	(d)	1							Ans. : (b)
1701
1702Q. 65	Chromatic number of cycle graph Cn, n > 1 and n is even 
1703(a)	2		(b)	3		(c)	4	(d)	1 							Ans. : (a)
1704Q. 66	Wheel graph chromatic number (n, n > 2 if n is odd
1705(a)	3		(b)	4 		(c)	2		(d)  1						Ans. : (a)
1706
1707Q. 67	Chromatic number of a wheel graph (n, n > 2 if n is even 
1708(a)	1		(b)	3		(c)	4		(d)  2						Ans. : (c)
1709
1710Q. 68	A graph which consists of only isolated vertex has chromatic number.
1711(a)	2		(b)	1		(c)	3		(d)  None of these			Ans. : (b)
1712Q. 69	A graph has one or more edges (without self loop) has a minimum chromatic number ?
1713(a)	2		(b)	3		(c)	4		(d)   1						Ans. : (a)
1714Q. 70	Every tree with two or more vertex has chromatic number. 
1715(a)	1		(b)	2		(c)	4		(d)   3						Ans. : (b)
1716Q. 71	A graph has chromatic number 2 if and only if it has no circuits of odd length.
1717(a)	True 	(b)	False											Ans. : (a)
1718Q. 72	If d is the maximum degree of the vertices in the graph G then chromatic number of G is 
1719(a)	( d + 1		(b)	( d + 1
1720(c)	( d  1		(d)	( d  1										Ans. : (a)
1721Q. 73	The minimum number of edges in a connected graph with n vertices
1722(a)	n  1		(b)	n 	(c)	n + 1 	(d)	None of these		Ans. : (a)
1723Q. 74	A graph is planar if and only if it does not contain
1724(a)	Subgraph homeomorphic to K3 and K3, 3 
1725(b)	Subgraph isomorphic to K5 or K3, 3
1726(c)	Subgraph isomorphic to K3 and K3, 3
1727(d)	Subgraph homeomorphic to K5 or K3, 3						Ans. : (d)
1728Q. 75	Maximum number of edges in a n-node undirected graph without self loop is
1729(a)	n2 	(b)		(c)	n  1	(d)  				Ans. : (b)
1730Q. 76	The vertex connectivity of K5 is,
1731(a)	2	(b)	3	(c)	4	(d)	1									Ans. : (c)
1732
1733Q. 77	If every edge of the graph G appears exactly once in the path then it is
1734(a)	Hamilton path 		(b)	Eulerian path 
1735(c)	Simple path 			(d)	Shortest path 					Ans. : (b)
1736Q. 78	If a graph possesses either zero or two vertices of odd degree then it is
1737(a)	Hamilton path 			(b)	Eulerian path 
1738(c)	Simple path			(d)	Shortest path 	 				Ans. : (b)
1739Q. 79	A connected graph having the degree of all vertices is even then it contains
1740(a)	Hamilton circuit 			(b)	Simple circuit 
1741(c)	Eulerian circuit 			(d)	None of these				Ans. : (c)
1742Q. 80	A directed graph possesses an Eulerian circuit if it is connected and the 
1743(a)	Incoming degree = outgoing degree
1744(b)	Incoming degree ( outgoing degree
1745(c)	Incoming degree > outgoing degree
1746(d)	Incoming degree < outgoing degree							Ans. : (a)
1747Q. 81	If every vertex of a graph is appearing exactly once then it is 
1748(a)	Hamilton path 		(b)	Eulerian path 
1749(c)	Simple path 		(d)	Shortest path 						Ans. : (a)
1750Q. 82	If G be a simple connected graph and sum of the degree of each pair of vertex ( (n  1) then it contains
1751(a)	Eulerian path 		(b)	Hamilton path
1752(c)	Simple path 		(d)	None								Ans. : (b)
1753Q. 83	For a connected graph having Hamilton circuit, which condition to be satisfied 
1754(a)	degree of each vertex = n  1 		(b)	degree of each vertex = n
1755(c)	d (v) ( n/2						(d)	d (v) = n + 1		Ans. : (c)
1756Q. 84	A simple graph in which there exists an edge between every pair of vertex is called 
1757(a)	Complete graph 		(b)	Euler graph 
1758(c)	Plannar graph 			(d)	Regular graph 				Ans. : (a)
1759Q. 85	The minimum number of spanning tree in a connected graph with n node is,
1760(a)	1	(b)	2	(c)	n  1	(d)	n/2								Ans. : (b)
1761Q. 86	If a graph require k different colours for its proper colouring.                  Then chromatic number of the graph is,
1762(a)	1		(b)	k		(c)	k  1		(d)	k/2					Ans. : (b)
1763Q. 87	The number of colours required to properly colour the vertices of every planar graph is
1764(a)	2		(b)	3		(c)	4		(d)  5						Ans. : (a)
1765Q. 88	Degree of each vertex in Kn is,
1766(a)	n		(b)	n  1	(c)	n  2 	(d)  2n  1					Ans. : (b)
1767Q. 89	Common data for Q. 90 to 92 Vertex V6 is called
1768
1769Fig. Q. 89
1770(a)	Pendant vertex 		(b)	Isolated vertex
1771(c)	Incident vertex		(d)	Adjacent  vertex					Ans. : (b)
1772Q. 90	Vertex V5 is called
1773(a)	Pendant 		(b)	Isolated 
1774(c)	Adjacent 		(d)	Incident								Ans. : (a)
1775Q. 91	Edge e4 is called 
1776(a)	Self loop 		(b)	Parallel edge	
1777(c)  Incident 		(d)	None									Ans. : (b)
1778Q. 92	edge e6 is called
1779(a)	Parallel edge 		(b)	Self loop 
1780(c)	Incident edge		(d)	None								Ans. : (b)
1781Q. 93	In a graph G d (Vi) = ?
1782(a)	e		(b)	2e		(c)	e/2		(d)   3e					Ans. : (b)
1783Q. 94	The number of vertices of odd degree in a graph is always.
1784(a)	Odd 		(b)	Even 	(c)	2e	(d)	None				Ans. : (b)
1785Q. 95	How many nodes are required to construct a graph with exactly 6 edges in which each node is of degree 2.
1786(a)	4	(b)	7	(c)	6	(d)	8									Ans. : (c)
1787					 
1788					
1789Q. 96	What is the number of edges in a graph with 6 nodes, 2 of degree 4 and 4 of degree 2.
1790(a)	6		(b)	8		(c)	7	(d)	5							Ans. : (b)
1791Q. 97	Whether K6 and K3, 3 are isomorphic ?
1792(a)	True 		(b)	False										Ans. : (b)
1793Q. 98
1794
1795Fig. Q. 98
1796G1 and G2 are isomorphic
1797True 		(b)	False											Ans. : (a)
1798Q. 99	Does the graph K1, 3  have Eulerian circuit ?
1799(a)	Yes 		(b)	No											Ans. : (b)
1800  
1801Q. 100	How many edges must a planar graph have if it has 7 regions and 5 nodes?
1802(a)	8		(b)	10			(c)	12			(d)	14				Ans. : (b)
1803Q. 101	How many number of regions defined by a connected planar graph with 6 nodes and 10 edges.
1804(a)	4	(b)	6	(c)	8	(d)	10									Ans. : (b)
1805Q. 102	A connected planar graph has nine vertices having degree 2, 2, 2, 2, 3, 3, 3, 4, 4, and 5.
1806How many edges are there ?
1807(a)	10		(b)	12		(c)	14	(d)	16						Ans. : (c)
1808Q. 103	In the same problem as in Q 102, how many regions ?
1809(a)	4	(b)	6	(c)	7	(d)	8									Ans. : (c)
1810Q. 104	Let G1 be a simple connected planar graph with 13 vertices and 19 edges. Thus the number of faces in the planner graph is 
1811(a)	6	(b)	8	(c)	9	(d)	13									Ans. : (b)
1812Q. 105	The maximum no. of edges in a planar graph is 
1813	(a)	3V  6	  	(b)	2 V  4		(c)	2e			(d)	None 	Ans. : (a)
1814Q. 106	The number of connected component in G is 
1815(a) n	(b) n + 2		(c) 2n/2		(d) 2n / n						Ans. : (b)
1816Q. 107	Which of the following graph has an Eulerian circuit ?
1817(a)	Any k-regular graph where K is an even numbers. 
1818(b)	A complete graph on 90 vertices.
1819(c)	The complement of a cycle on 25  vertices.
1820(d)	None of these 												Ans. : (a)
1821Q. 108	Which of the following statements in true for every planar graph on n vertices. 
1822(a)	The graph is connected 	
1823(b) 	The graph is Eulerian 
1824(c)	The graph has vertex-cover of size at most 3n/4
1825(d)	The graph has an independent set of size at least n/3.		Ans. : (a)
1826Q. 109	What is the number of vertices in an undirected graph with 27 edges, 6 vertices of degree 2, 3 vertices of degree 4 and remaining of degrees 3 ?
1827(a) 10	(b) 11	(c) 18	(d) 19 									Ans. : (d)
1828Q. 110	Consider the graph shown below. The vertex connectivity of the graph is
1829
1830
1831Fig. Q. 110
1832(a)	1	(b)	2	(c)	3	(d)	4									Ans. : (b)
1833Q. 111	Consider the graph shown below. The edge connectivity of the graph is
1834
1835Fig. Q. 111
1836(a)	1	(b)	2	(c)	3	(d)	4									Ans. : (a)
1837Q. 112	The edge connectivity for the complete graph K6 is 
1838(a)	5	(b)	3	(c)	2	(d)	4									Ans. : (a)
1839Q. 113	The vertex connectivity for the complete bipartite graph K3,4 is 
1840(a)	1	(b)	4	(c)	3	(d)	2									Ans. : (c)
1841Q. 114	A graph which has an Hamilton circuit is called 
1842(a)	Hamilton graph		(b)	Complete bipartite graph
1843(c)	Eulurian graph 		(d)	None of these						Ans. : (a)
1844Q. 115	The complete bipartite graph K2,4 has
1845(a)	Eulurian circuit		(b)	Hamilton circuit
1846(c)	neither eulurian nor Hamilton circuit	
1847(d)	both eulurian nor Hamilton circuit						Ans. : (**)
1848Q. 116	Consider the following graph. It has
1849(a)	Eulurian circuit		(b)	Hamilton circuit
1850(c)	both				(d)	neither		 
1851										                      Fig. Q. 116	Ans. : (b)
1852
1853Q. 117	Consider the following graph. It has
1854(a)	Eulurian circuit		(b)	Hamilton circuit
1855(c)	both				(d)	neither					   Fig. Q. 117	Ans. : (d)
1856Q. 118	The minimum number of colors required to produce a proper coloring of a simple connected graph G is called
1857(a)	chromatic number of G		(b)	edge connectivity of G.
1858(c)	Vertex connectivity of G		(d)	none of these				Ans. : (a)
1859Q. 119	If a graph G is isomorphic to its complement then G is called
1860(a)	complete graph				(b)	bipartite graph
1861(c)	Self complementary graph	(d)	None of these				Ans. : (c)
1862
1863Q. 120	Consider the graph G1 and G2 below. Then G1 U G2 is 	
1864
1865Fig. Q. 120
1866
1867
1868
1869(a)								(b)
1870		
1871
1872		
1873(c)								(d)									Ans. : (b)
1874	
1875					
1876Q. 121	In the previous quertion G1 n G2 is 	
1877(a)								(b)		
1878
1879		
1880
1881
1882(c)								(d)									Ans. : (c)
1883	
1884			
1885Q. 122	Consider the following graph, the vertex connectivity is  	
1886(a)	1	(b)	2	(3)	4	(d)	3									Ans. : (b)
1887
1888Fig. Q. 122
1889Q. 123	Consider the following graph and find the edge connectivity of the graph	
1890(a)	1	(b)	3	(3)	2	(d)	4									Ans. : (b)
1891
1892
1893
1894Fig. Q. 123
1895Q. 124	Consider the graph G1 and its subgraph G2.
1896
1897
1898Fig. Q. 124
1899Then subgraph G2 is called
1900(a)	complete subgraph			(b)	regular subgraph
1901(c)	spanning subgraph			(d)	none of these				Ans. : (c)
1902Q. 125	Consider the graph G and its subgraph H1 and H2.
1903
1904Fig. Q. 125
1905Then H1 and H2 are.
1906(a)	Vertex disjoint subgraph	(b)	spanning subgraphs
1907(c)	Regular subgraphs  			(d)	none of these				Ans. : (a)
1908Q. 126	Consider the following graph G and its subgraph H1 and H2.
1909
1910Fig. Q. 126
1911Then H1 and H2 are.
1912(a)	vertex disjoint		(b)	edge disjoint
1913(c)	spanning   			(d)	none of these						Ans. : (b)
1914Q. 127	The adjacency matrix for the following graph is
1915
1916Fig. Q. 127
1917(a)			(b)	
1918
1919(c)			(d)					Ans. : (a)
1920
1921Q. 128	If G is a simple graph on n vertices and the degree of each vertex is 
1922(n  1) then the graph is :
1923(a)	bipartite graph		(b)	null graph
1924(c)	complete graph 		(d)	None of these 						Ans. : (c)
1925 	
1926Q. 129	In the following graph, the adjacent vertex are : 
1927(a)	e1 and e3		(b)	e2 and e5
1928(c)	e1 and e4		(d)	None of these							Ans. : (b)
1929
1930Fig. Q. 129
1931Q. 130	In the following graph, the adjacent vertex are
1932(a)	v1 and v2		(b)	v2 and v4
1933(c)	v1 and v3		(d)	None of these
1934							   Fig. Q. 130
1935										  Ans. : (a)
1936Q.1. A graph G is called a..... if it is a connected acyclic graph
1937A. Cyclic graph
1938B. Regular graph 
1939C. Tree 
1940D. Not a graph 
1941ANSWER: C
1942
1943Q.2. In an undirected graph the number of nodes with odd degree must be
1944A. zero
1945B. odd
1946C. prime
1947D. even
1948ANSWER: D
1949
1950Q.3. A graph is a collection of
1951A. Row and columns 
1952B. Vertices and edges 
1953C. Equations
1954D. None of these 
1955ANSWER: B
1956
1957Q.4. An undirected graph possesses an eulerian circuit if and only if it is connected.
1958A. all of even degree
1959B. all of odd degree
1960C. of any degree
1961D. even in number
1962ANSWER: A
1963
1964Q.5. The number of colors required to properly color the vertices of every planer graph is
1965A. 2
1966B. 3
1967C. 4
1968D. 5
1969ANSWER: D
1970
1971Q.6. In a graph if e=(u, v) means 
1972A. u is adjacent to v but v is not adjacent to u 
1973B. e begins at u and ends at v 
1974C. u is processor and v is successor 
1975D. both b and c 
1976ANSWER: D
1977
1978Q.7. A minimal spanning tree of a graph G is
1979A. A spanning sub graph 
1980B. A tree 
1981C. Minimum weights 
1982D. All of above 
1983ANSWER: D
1984
1985Q.8. A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are
1986A. greater than n–1
1987B. less than n(n–1)
1988C. greater than n(n–1)/2
1989D. less than n2/2
1990ANSWER: A
1991
1992Q.9. In any undirected graph the sum of degrees of all the nodes 
1993A. Must be even 
1994B. Are twice the number of edges
1995C. Must be odd 
1996D. Need not be even 
1997ANSWER: B
1998
1999Q.10. A graph with one vertex and no edges is
2000A. multigraph
2001B. digraph
2002C. isolated graph
2003D. trivial graph
2004ANSWER: D
2005
2006Q.11.Choose the most appropriate definition of plane graph 
2007A. A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices 
2008B. A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y 
2009C. A simple graph which is Isomorphic to Hamiltonian graph 
2010D. None of these 
2011ANSWER: A
2012
2013Q.12. A graph with n vertices will definitely have a parallel edge or self loop of the total number of edges are
2014A. more than n
2015B. more than n+1
2016C. more than (n+1)/2
2017D. more than n(n-1)/2
2018ANSWER: D
2019
2020Q.13. Which one of the following statements is incorrect ?
2021A. The number of regions corresponds to the cyclomatic complexity.
2022B. Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph.
2023C. Cyclometric complexity for a flow graph G is V(G) = E–N+2, where E is the number of edges & N is the number of nodes in the flow graph.
2024D. Cyclometric complexity for a flow graph G is V(G) = P + 1, where P is the number of predicate nodes contained in the flow graph G.
2025ANSWER: B
2026
2027Q.14. The maximum degree of any vertex in a simple graph with n vertices is
2028A. n-1
2029B. n+1
2030C. 2n-1
2031D. n
2032ANSWER: A
2033
2034Q.15. The complete graph with four vertices has k edges where k is
2035A. 3
2036B. 4
2037C. 5
2038D. 6
2039ANSWER: D
2040
2041Q.16. Suppose v is an isolated vertex in a graph, then the degree of v is
2042A. 0
2043B. 1
2044C. 2
2045D. 3
2046ANSWER: A
2047
2048Q.17. A graph in which all nodes are of equal degree is called
2049A. Multi graph 
2050B. Non regular graph 
2051C. Regular graph 
2052D. Complete graph 
2053ANSWER: C
2054
2055Q.18. Two isomorphic graphs must have 
2056A. Equal number of vertices 
2057B. Same number of edges
2058C. Same number of vertices 
2059D. All of the above 
2060ANSWER: D
2061
2062Q.19. Graphs are represented using 
2063A. Adjacency tree 
2064B. Adjacency linked list 
2065C. Adjacency graph 
2066D. Adjacency queue 
2067ANSWER: B
2068
2069Q.20. If every node u in G is adjacent to every other node v in G, A graph is said to be 
2070A. Isolated
2071B. Complete
2072C. Finite
2073D. Strongly Connected
2074ANSWER: B
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088Sr No	Question	Option 1	Option 2	Option 3	Option 4	Correct Option
20891	Let A = {2, {4, 5}, 4}. Which statement is correct?	a) 5 is an element of A.	b) {5} is an element of A.	c) {4, 5} is an element of A.	c) {5} is a subset of A. 	C 
20902	Which of these sets is finite?	a) {x | x is even}	b) {x | x < 5}	c) {1, 2, 3,...}	d) {1, 2, 3,...,999,1000}	d
20913	Which of these sets is not a null set?	a) A = {x | 6x = 24 and 3x = 1}	b) B = {x | x + 10 = 10}	c) C = {x | x is a man older than 200 years}	d) D = {x | x < x}	b
20924	Let D      E. Suppose a        D and b      E. which of the following statements must be true.	c    D	b    D	a    E	a    D	C 
20935	Let A = {x | x is even}, B = {1, 2, 3,..., 99, 100}, C = {3, 5, 7, 9}, D = {101, 102} and E = {101, 103, 105}. Which of these sets can equal S if S A and S and B are disjoint? 	a) A         	b) B 	c) C 	d) E	d
20946	Which set S does the power set 2S = {         , {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} come from?	a) {{1},{2},{3}}	b) {1, 2, 3}	c) {{1, 2}, {2, 3}, {1, 3}}	d) {{1, 2, 3}} 	d
20957	Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct? 	a) A       B = {v, w, x, y, z} 	b) A         B = {v, w, y, z} 	c) A      B = {v, w, x, y} 	d) A        B = {x, w, x, y, z} 	a
20968	Let A = {1, 2, 3, ..., 8, 9} and B = {3, 5, 7, 9}. Which of the following statements is correct?. 	a) A          B = {2, 4, 6} 	b) A         B = {1, 2, 3, 4, 5, 6, 7, 8, 9} 	c) A        B = {1, 2, 4, 6, 8} 	d) A           B = {2, 4, 6, 8} 	d
20979	. Let A = {2, 3, 4}, B = {3} and C = {x | x is even}. Which statement is correct? 	a) C         A=B	b) C          B=A	c) A         C	d) C / A = B 	a
209810	Let A          B, B         C and D        A = C. Which statement is always false? 	a) B       D	b) A          C	c) A = B 	d) B       D=           AND B          A	d
209911	What is shaded in the Venn diagram above?.                                                                              	a) A           B	b) A          B	c) A 	d) B 	b
210012	 What is shaded in the Venn diagram below?. 	a) A       B	b) A' 	c) A - B 	d) B - A 	D
210113	Let U = {1, 2, 3, ..., 8, 9} and A = {1, 3, 5, 7}. Find A'. 	a) A' = {2, 4, 6, 8} 	b) A' = {2, 4, 6, 8, 9} 	c) A' = {2, 4, 6} 	d) A' = {9}	b
210214	Find the ordered pairs corresponding to the points A and B, which appear in the coordinate diagram {1, 2, 3} × {1, 2, 3} below.	a) A = (2, 1), B = (1, 3)	b) A = (1, 2), B = (3, 1)	c) A = (3, 1), B = (1, 2)	d) A = (2, 2), B = (2, 3)	b
210315	Let R be the set of real numbers and let the function f : R        R be defined by f (x) = x - 2. Which ordered pair belongs to the graph f * of the function f ?	a) (5, 6)	b) (3, 2)	c) (5, 3)	d) (4, 1)	C 
210416	Let S = {a, b, c, d}. Which of the following sets of ordered pairs is a function of S into S?	a) {(a, b), (c, a), (b, d), (d, c), (c, a)}	b) {(a, c), (b, c), (d, a), (c, b), (b, d)}	c) {(a, c), (b, d), (d, b)}	d) {(d, b), (c, a), (b, e), a, c)}	a
210517	Let M = {1, 2, 3}, and let the relation R in M be the set of points displayed in the coordinate diagram of M × M. Which one of the following statements is true?	a) 1 R 1	b) 3 R 2	c) 2 R 2	d) 2 R 1 	d
210618	The relation R is given by the set of ordered pairs, R = {(2, 4), (3, 4), (1,3), (3, 5), (2, 3) }. Which of the following is the domain of R?	a) {2, 3, 1, 5}	b) {1, 2, 3}	c) {1, 2, 3, 4, 5}	d) {2, 4, 3, 5}	b
210719	Let R be the relation as in Q 3, R = {(2, 4), (3, 4), (1,3), (3, 5), (2, 3)} . What should the range of R be?	a) {3, 4, 5}	b) {1, 2, 3}	c) {1, 2, 3, 4, 5}	d) {4, 4, 2, 5}	a
210820	Find the inverse of the relation R = {(2, 4), (3, 4), (1,3), (3, 5), (2, 3)} .	a) {(2, 4), (3, 4), (1, 3), (3, 5), (2, 3)}	b) {(4, 2), (4, 3), (3, 1), (5, 3), (3, 2)}	c) {5, 4, 3, 2, 1}	d) {(4, 4), (3, 3), (1, 1), (5, 5), (2, 2)}	b
210921	Which one of the following open sentences defines a reflexive relation on the set of natural numbers?	a) "x is less than y"	b) "x = 2y"	c) "x - y = 5"	d) "x divides y"	d
211022	. Find the reflexive relation on the set A if A = {a, b, c} .	a) R1 = {(a, b), (b, c), (a, a), (c, c)}	b) R2 = {(a, a), (b, c), (c, c)}	c) R3 = {(a, a), (a, c), (c, a), (b, b), (c, c)}	d) R4 = {(a, a), (c, c), (a, c), (c, a)}	C 
211123	Which one of the following open sentences defines a symmetric relation in the set of natural numbers N?	a) "x is less than y"	b) "xy = 12"	c) "x - y = 5"	d) "x divides y"	b
211224	Find non-symetric relation on the set B = {c, d, e}.	a) R1 = {(e, e)}	b) R2 = {(e, e),(c, d), (d, c)}	c) R3 = B x B	d)R4 = {(c, d), (d, d), (d, e)}	d
211325	Find the anti-symmetric relation on the set B = {1, 2, 3}.	a) R1 = {(3, 3)}	b) R2 = {(1, 2), (1, 1), (1, 3), (2, 1)}	c) R3 = B × B	d) R4 = {(1, 2), (2, 2), (2, 3), (3, 2)}	a
211426	Let C = {1, 2, 3, 4}and let R1, R2, R3, R4 be the relations in C. Which one of them is transitive?	a) R1 = {(2, 3), (3, 2), (3, 3), (1, 1)}	b) R2 = {(1, 1), (2, 2), (1, 3), (3, 2)}	c) R3 = {(3, 4), (3, 3), (4, 4), (4, 3)}	d) R4 = {(1, 2), (2, 2), (2, 3), (3, 2)}	C 
211527	Find the transitive relation in the set D = {1, 2, 3, 4}.	a) R1 = {(1, 2), (4, 3), (3, 2), (2, 4)}	b) R2 = {(1, 4), (4, 2), (1, 1), (3, 2)}	c) R3 = {(3, 2), (2, 4), (4, 4), (4, 3)}	d) R4 = {(3, 1), (2, 4), (4, 3), (3, 4)}	d
211628	Which of the diagrams defines a function of A = {a, b, c, d} into B = {1, 2, 3}	a)	b)	c)	d)	b
211729	Let f 1, f 2, f 3, f 4, f 5 be functions of R into R and let f 1(x) = x2 + 3x - 4. Which of these functions are equal to f 1?	a) f2(x) = x2	b) f3(y) = y2 - 4	c) f4(z) = z2 + 3z - 4	d) f5(x) = x2 + 3x	C 
211830	The negation symbol is denoted by______.	a. 	b. →	c. ↔	d. v	a
211931	P           P is a _____.	a. contradiction.	b. tautology.	c. conditional.	d. biconditional.	a
212032	If there are n distinct components in a statement then there is_________ combinations of values in the truth table.	a. n+1.	b. n2.	c. 2n.	d. n+2.	C 
212133	If P then Q is called _________ statement.	a. conjunction.	b. disjunction.	c. conditional.	d. biconditional.	C 
212234	(p→q)→(^q) is __________.	a. tautology .	b. contradiction .	c. WFF.	d. not a WFF.	d
212335	A relation R in a set X is symmetric if ________.	a. yRx.	b. xRy, yRx.	c. xRy, yRz => xRz.	d. xRy => yRx.	d
212436	. If a relation is reflexive, then all the diagonal entries must be ________.	a. 0.	b. 1.	c. 2.	d. -1.	b
212537	If R is reflexive, symmetric and transitive then a relation is said to be ________.	a. binary relation.	b. compatibility relation.	c. equivalence relation.	d. partial order relation.	C 
212638	The set of all finite words over E is denoted by ________.	a. E.	b. E+.	c. E*.	d. λ.	b
212739	Surjective function is also called ________.	a. one-one.	b. one to one.	c. into.	d. onto.	d
212840	One to one onto function is also called __________.	a. bijective.	b. injective.	c. surjective.	d. composition function.	a
212941	(gof)-1 =________.	a. g-1 .	b. f-1 .	c. g-1 o f-1.	d. f-1 o g-1.	d
213042	The composition of function is associative but not _______.	a. idempotent.	b. commutative.	c. distributive.	d. de-morgan’s.	b
213143	. A mapping x into itself is called __________.	a. relation.	b. equivalence relation.	c. reflexive.	d. transformation.	C 
213244	. Which one of the following is Idempotent law?	a. PVF           P.	b. P^T             P.	c. P^P              P.	d. P^F              F.	C 
213345	The duality law of (P^Q)vT is ________.	a. (P^Q)^T.	b. (PvQ)^T .	c. (PvQ)vF .	d. (PvQ)^F.	d
213446	A product of the variables and their negations in a formula is called _________.	a. elementary product.	b. elementary sum.	c. DNF.	d. CNF.	a
213547	Any vertex having degree one is called _______.	a. simple vertex.	b. pendant vertex.	c. regular vertex.	d. complete vertex.	b
213648	A graph that has neither self loops nor parallel edges is called_____.	a. regular graph.	b. complete graph.	c. isolated graph.	d. simple graph.	d
213749	. A graph in which every vertex has same degree is called _________.	a. regular graph.	b. complete graph.	c. isolated graph.	d. simple graph.	a
213850	Kn denotes _______.	a. regular graph.	b. complete graph.	c. isolated graph.	d. simple graph.	b
213951	The number of vertices of odd degree in a graph is always________.	a. odd.	b. even.	c. zero.	d. one.	b
214052	A path of a graph is said to be ______ if it contains all the edges of the graph.	a. eulerian.	b. hamiltonian.	c. tournament.	d. planar.	a
214153	Traveling salesman problem is example for_______.	a. euler graph.	b. hamiltonian graph.	c. tournament.	d. planar graph.	b
214254	If a node v is reachable from node u then the path of minimum length u to v is called _____.	a. reachability.	b. node base.	c. geodesic.	d. accessibility.	C 
214355	P→ Q , Q→ R= ________.	a. P→ R.	b. R→ P.	c. Q.	d. R.	a
214457	The symbol  which reads ‘for all’ is _______.	a. universal quantifier.	b. existential quantifier.	c. proportional quantifier.	d. logical quantifier.	a
214558	Which of the following is a tautology?	a. (P v Q) → P.	b. P v ( Q → P).	c. P v ( P → Q).	d. P → (Q → P).	C 
214659	The proposition of P       (      P^Q)           is _______.	a. a tautology.	b. a contradiction.	c. logically equivalent to P   Q	d. logically equivalent to P      Q	C 
214760	(P    P)          ( P → (Q    Q)) is equivalent to _______.	a. P → Q.	b. P      Q	c. P      Q	d. Q → P.	C 
214861	Given that (P          Q)         (    P          Q) is false, the truth values of P & Q are _______.	a. both false.	b. both true.	c. P true & Q false.	d. P false & Q true.	a
214962	The ‘Subset’ relation on a set of sets is ________.	a. partial ordering.	b. an equivalence relation.	c. transitive and symmetric only.	d. transitive and anti-symmetric only.	a
215063	A relation R is defined on the set of integers as xRy if and only if (x+y) is even.Which of the following statement is TRUE?	a. R is not an equivalence relation.	b. R is an equivalence relation having one equivalence classes.	c. R is an equivalence relation having two equivalence classes.	d. R is an equivalence relation having three equivalence classes.	C 
215164	Let R1& R2 be two equivalence relations on a set. Consider the following assertions:(i) R1  R2 is an equivalence relation.(ii) R1 >= R2 is an equivalence relation.Which of the following is correct?	a. Both assertions are true.	b. Assertion (i) is true but assertion (ii) is not true.	c. Assertion (ii) is true but assertion (i) is not true.	d. Neither (i) nor (ii) is true.	C 
215265	If R = {(1, y), (1, z), (3, y)} then R-1 = ___________.	a. {(1, a), (y, z)}.	b. {(y, z), (z, a), (y, c)}.	c. {(y, a), (1, z), (3, y)}.	d. {(y, a), (z, a), (3, y)}.	b
215366	Let R ={ (a,b),(c,d),(b,b)}, S = {(d,b),(c,b),(a,d)} then R ° S = ___________.	a. {(a,e),(c,b),(b,e)}.	b. {(d,b),(c,b),(a,d)}.	c. {(a,b),(b,b)}.	d. {(c,b)}.	a
215467	Let R and s be two relations on a set of positive integers I & R = {(a, 3a+a) / a Є I},S = {(a,a+a)/ a Є I} then R ° R ° R = __________.	a. {(a,3a+a)/ a Є I}.	b. {(a,9a+a)/ a Є I}.	c. {(a,27a+a)/ a Є I}.	d. {(a,9a+c)/ a Є I}.	C 
215568	The number of relations from A = {a,b,c} to B = {1,2} are __________.	a. 6.	b. 23.	c. 25.	d. 26.	d
215669	(A X B)         (A X C) = ___________.	a. A X (B         C).	b. A X (B       C).	c. A X B X C.	d. A         (B X C).	b
215770	The minimum number of edges in a connected graph with n vertices is ___________.	a. n-1.	b. n.	c. n+1.	d. n2.	a
215871	A graph is planar if and only if does not contain ________.	a. subgraphs homeomorphic to k3 & k3,3.	b. subgraphs isomorphic to k5 or k3,3.	c. subgraphs isomorphic to k3 & k3,3.	d. subgraphs homeomorphic to k5 or k3,3.	d
215972	Maximum number of edges in an n-node undirected graph without self loops is ____.	a. n 2.	b. [n(n-a.]/2.	c. n-1.	d. [n(n+a.]/2.	b
216073	In any undirected graph the sum of degrees of all the vertices ________.	a. must be even.	b. is twice the number of edges.	c. must be odd.	d. can be even or odd.	d
216174	The total number of edges in a complete graph of n vertices is _________.	a. n.	b. n/2.	c. n2-1.	d. [n(n-1]/2.	d
216275	A directed complete graph of n vertices contains __________.	a. one arrow between each pair of distinct vertices.	b. two arrows between each pair of distinct vertices.	c. n-1 arrows between each pair of distinct vertices.	d. path between every two distinct vertices.	a
216376	A directed graph G = (V, E) is said to be finite if its ________.	a. set V of vertices is finite.	b. set V of vertices & set E of edges are finite.	c. set E of edges are finite.	d. no vertices & edges are repeated.	b
216477	Let R = {(3, 3), (6, 6), (9, 9), (1,2), (1,6), (6, 1), (3, 9), (3, 1), (3, 6)} be a relation onthe set A = {3, 6, 9, 12}. The relation is _________	a. reflexive and transitive.	b. reflexive.	c. an equivalence relation.	d. reflexive and symmetric.	a
216579	If a compound statement is made up of three simple statements then the number of rows in the truth table is _______.	a. 2.	b. 4.	c. 6.	d. 8.	d
216680	The conditional statement P→Q is equivalent to _____.	a. Pv Q.	b.       Pv     Q	c. Pv        Q	d. P ΛQ.	b
216781	Let R={(1,b.,(3,d.,(2,b.} and S={(4,b.,(2,5),(3,a.} be a relation then R•S=____.	a. {(1,b.,(3,d.,(2,b.}.	b. {(1,5),(3,b.,(2,5)}.	c. {(4,b.,(2,5),(3,a.}.	d. {(1,d.,(3,b.,(2,c.}.	b
216882	Let R={(1, 3), (4, 2), (2, 2), (3, 3), (1, 1),(4,4)} be a relation on the set A={1, 2, 3, 4}.The relation R is ________.	a. a function.	b. reflexive.	c. not symmetric.	d. transitive.	C 
216983	The statement p → (q → p) is equivalent to ________.	a. p → (p → q).	b. p→ (p ∨ q).	c. p→ (p ∧ q).	d. p → (p ↔ q).	b
217084	If a relation is reflexive then in the graph of a relation there must be a loop at _____.	a. two nodes.	b. only one nodes.	c. three nodes.	d. each node.	d
217185	An undirected graph is tripartite if and only if it has no circuits of _______ lengths.	a. odd.	b. even.	c. distinct.	d. equal.	a
217286	A graph is bipartite if and only if its chromatic number is ________.	a. 1.	b. 2.	c. even.	d. odd.	b
217387	G is strongly connected implies _________.	a. G is unilaterally connected.	b. G is bilaterally connected.	c. G is unilaterally connected.	d. G has more than one component.	a
217488	For a symmetric digraph, the adjacency matrix is _________.	a. symmetric.	b. asymmetric.	c. antisymmetric.	d. symmetric or antisymmetric.	a
217589	The total number of degrees of an isolated node is _______.	a. 0.	b. 1.	c. odd.	d. even.	a
217690	If G is a connected planar graph then it has a vertex of degree _______.	a. 3 or less.	b. 4 or less.	c. 5 or less.	d. 6 or less.	C 
217791	The less than relation < on real is __________.	a. a partial ordering since it is asymmetric and reflexive.	b. a partial ordering since it is anti-symmetric and reflexive.	c. not a partial ordering since it is not asymmetric and not reflexive.	d. not a partial ordering since it is not anti-symmetric and not reflexive.	d
217892	A minimal non-empty edge –cut of G is called a _________.	a. bond.	b. cycle.	c. path.	d. tour.	a
217993	A connected graph that has no cut vertices is called a ________.	a. bond.	b. block.	c. path.	d. tour.	b
218094	A set containing no element is called ____________.	a. null set.	b. unit set .	c. infinite set.	d. finite set.	a
218195	A = {1,3,5,7,9} is a __________.	a. finite set .	b. infinite set.	c. singleton set.	d. null set .	a
218296	The number of Indians in the world is _________.	a. infinite.	b. finite.	c. universal .	d. sub-set.	b
218397	When each element of A is an element of B and each element of B is an element of A, the sets are known as _________.	a. subsets.	b. properties of subsets.	c. equal sets.	d. universal sets.	C 
218498	If two sets contain the same distinct elements then it is __________.	a. singleton set .	b. equal set.	c. universal set.	d. none.	b
218599	A={1,6,3}, B={2,3,5}, A∩B = ____________.	a. {1,2}.	b. {3}.	c. {6,5}.	d. {6,2}.	C 
2186100	If A={0,1,2,3,4,5,6}, B={0,2,4,6,8} then A∩B is ____________ .	a. {0,2,4,6}.	b. {1,2,4,6}.	c. {4,6,8}.	d. {3,4,8}.	a
2187101	If A= {0,1,2,3,4,5,6}, B={0,2,4,6} and C={0,3,6,9}, A∩B∩C = _________.	a. {0,1,2,3,4,5,6,9}.	b. {0,6}.	c. {0}.	d. {1}.	b
2188102	n(A∪B) is __________.	a. N .	b. 0.	c. n(A)+n(B)-n(A∩B).	d. none.	C 
2189103	If A= {2, 7, 3}, B= {4, 5}, AUB= __________.	a. {7}.	b. {3, 4, 5}.	c. {2, 7, 3, 4, 5}.	d. {3}.	C 
2190104	If A={a,b,c,d}, B={a,e,i} and C={b,c,d,e}, AUBUC= _________.	a. 0.	b.{i}.	c.{a,b,c,d,e,i}.	d.{a,e,b}.	C 
2191105	Two sets which have no common elements is said to be ________.	a. disjoint set.	b. equal set .	c. singleton set.	d. universal set.	a
2192106	n(φ) = _________.	a. 0.	b. 1.	c. 2.	d. 3.	a
2193107	If in the truth table the answer column has the truth values both TRUE and FALSE then it is said to be ________.	a. tautology.	b. contradiction.	c. neither tautology nor contradiction.	d. tautology and contradiction.	C 
2194108	Let R={(1,b.,(3,d.,(2,b.} and S={(4,b.,(2,5),(3,a.} be a relation then RοS=____.	a. {(1,b.,(3,d.,(2,b.}.	b. {(1,5),(3,b.,(2,5)}.	c. {(4,b.,(2,5),(3,a.}.	d. {(1,d.,(3,b.,(2,c.}.	b
2195109	The binary relation R = {(0, 0), (1, a.} on A = {0, 1, 2, 3, } is _______.	a. reflexive, not symmetric, transitive.	b. not reflexive, symmetric, transitive.	c. reflexive, symmetric, not transitive.	d. reflexive, not symmetric, not transitive.	b
2196110	Define a binary relation R = {(0, a., (1, b., (2, c., (3, b., (2, 0)} on A = {0, 1, 2, 3} The directed graph (including loops) of the transitive closure of this relation has ______.	a. 16 arrows.	b. 12 arrows.	c. 8 arrows.	d. 6 arrows.	a
2197111	If f(x)= 2x + 3 and g(x)= 4x then fog is ___________.	a. 8x2 + 3.	b. 8x + 3.	c. 8x3 + 3.	d. 8x4 + 3.	b
2198112	If an edge e is said to join the vertices u and v then the vertices u and v are called __.	a. initial vertices.	b. terminal vertices.	c. ends of e.	d. all the above.	C 
2199113	Edges intersect only at their ends are called ________.	a. planar.	b. loop.	c. link.	d. non planar.	a
2200114	Two vertices which are incident with the common edge are called __________ as are two edges which are incident with the common vertex.	a. distinct.	b. directed.	c. adjacent.	d. loops.	C 
2201115	An edge with identical ends is called _________.	a. complete graph.	b. bipartite graph.	c. loops.	d. link.	C 
2202116	An edge with the distinct ends is called ___________.	a. complete graph.	b. bipartite graph.	c. loops.	d. link.	d
2203117	A simple graph in which each pair of distinct vertices is joined by an edge is called a__________.	a. empty graph.	b. complete graph.	c. simple graph.	d. bipartite graph.	C 
2204118	The graph is said to be a simple graph if it has _________.	a. no links.	b. no loops.	c. no vertices.	d. no edges.	b
2205119	Each edge has one end in X and one end in Y then the graph (X, Y) is called _____.	a. simple.	b. empty.	c. complete.	d. bipartite.	d
2206120	The graph defined by the vertices and edges of a __________ is bipartite.	a. square.	b. cube.	c. single.	d. both (a) and (b).	b
2207121	Which of the following statements is true?	a. A number is rational if and only if its square is rational.	b. An integer n is odd if and only if n2 + 2n is odd.	c. A number is irrational if and only if its square is irrational.	d. A number n is odd if and only if n(n + a. is even.	b
2208122	To any graph G there corresponds a v × € matrix is called ________.	a. incidence matrix.	b. adjacency matrix.	c. square matrix.	d. null matrix.	a
2209123	If H is a sub graph of G then G is a ______ of H.	a. proper sub graph.	b. induced sub graph.	c. spanning sub graph.	d. super graph.	d
2210124	If the graph G1 and G2 has no vertex in common then it is said to be ______.	a. disjoint.	b. edge disjoint.	c. union .	d. intersection.	a
2211125	The degree of vertex v in G is __________.	a. number of edges of G incident with v.	b. number of loops in G.	c. number of links in G.	d. number of sub graph in G.	a
2212130	Which of the following statements is TRUE?	a. For all sets A, B, and C, A − (B − C) = (A − B) − C.	b. For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B.	c. For all sets A, B, and C, (A − B) ∩ (C − B) = A − (B U C).	d. For all sets A, B, and C, if A ∩ C = B ∩ C then A = B.	b
2213131	If a statement is P: I went to my class yesterday. Then ┐P is ___________.	a. i did not go to my class yesterday.	b. i was absent to my class today.	c. it is not the case that I went to my class today.	d. i will not go to class today.	a
2214132	 If the truth value of P is false then the truth value of negation P is ________.	a. true.	b. false.	c. true or false.	d. true and false.	a
2215133	The conjunction of the statement is formed by introducing _________.	a. OR.	b. NOT.	c. AND.	d. IF.	C 
2216134	If the statements are given by P: It is raining today, Q: There are 20 tables in this room then P ٨Q is ______________.	a. if it is raining today then there are 20 tables in this room.	b. it is raining today and there are 20 tables in this room.	c. it is raining today or there are 20 tables in this room.	d. it is raining today but there are 20 tables in this room.	b
2217135	If the statements are given by P: It is raining today, Q: London is a city. Then P^ ┐Q is ____________.	a. it is raining today and London is a city.	b. it is raining today but London is not a city.	c. it is raining today and London is not a city.	d. if it is raining today then London is not a city.	C 
2218136	If the statement P has the truth value T and Q has the truth value F then P٧Q is ___.	a. T.	b. F.	c. T and F.	d. None.	b
2219137	If the statement P has the truth value T and Q has the truth value F then P٨Q is ___.	a. T.	b. F.	c. T and F.	d. None.	b
2220138	The negation of ┐ (P ٨ Q)٧ R is __________.	a. ┐(P ٨ Q)٨ R.	b. ┐(P ٧ Q)٧ R.	c. ┐(P ٨ Q)٧┐R.	d. (P ٨ Q)٧ R.	C 
2221139	The negation of (P٨Q)٧(Q٨R) is _________.	a. ┐ (P٨Q)٧┐(Q٨R).	b. ┐(P٨Q)٨┐(Q٧R).	c. ┐ (P٧Q)٨┐(Q٨R).	d. ┐(P٨Q)٧┐(Q٧R).	a
2222140	For every possible truth values of P, the truth value of P٨┐P is __________.	a. T.	b. F.	c. T and F.	d. None.	b
2223141	Which of the following statement is tautology?	a. (P ٨ Q)٧ Q.	b. (P ٧ Q)٨ Q.	c. (P ٧ Q)٨ ┐P.	d. (P ٧ Q)٧┐P.	d
2224142	The symbolic form for the statement, Mark is poor or he is both rich and unhappy is __________.	a. ┐R٧(R٨┐H).	b. R٨┐(R٨┐H).	c. ┐R٧ (R٧┐H).	d. ┐R٨ (R٨┐H).	a
2225143	The conditional statement is formed by introducing ____________.	a. P and Q.	b. P or Q.	c. P if and only if Q.	d. If P then Q.	d
2226144	The Bi-conditional statement is formed by introducing ________.	a. P and Q.	b. P or Q.	c. P if and only if Q.	d. If P then Q.	C 
2227145	If P has the truth value t and Q has truth value F then P→Q is __________.	a. T.	b. F.	c. T or F.	d. T and F.	b
2228146	Which one of the following statement is example of P→Q?	a. the sun is shining today but 2+7>4.	b. if the sun is shining today, then 2+7>4.	c. the sun is shining today and 2+7>4.	d. the sun is shines today if and only if 2+7>4.	b
2229147	Which one of the following is the example of P↔Q?	a. the sun is shining today but 2+7>4.	b. if the sun is shining today, then 2+7>4.	c. the sun is shining today and 2+7>4.	d. the sun is shines today if and only if 2+7>4.	d
2230148	P is equivalent to __________.	a. ┐┐P.	b. P٧P.	c. P٨P.	d. Both (a) and (b).	a
2231149	(P٨┐P)٧P is equivalent to ____________.	a. P.	b. Q.	c. ┐P.	d. ٧Q.	b
2232150	P٧┐P is equivalent to ___________.	a. ┐P٧┐P.	b. P٨┐P.	c. Q٧┐Q.	d. Q٨┐Q.	C 
2233151	Which one of the following is well formed formula?	a. (P→Q) →(٨Q).	b. (P٨Q)→Q.	c. (P٨Q)→Q).	d. ((P٨Q)→Q).	b
2234152	Which of the following statement is the negation of the statement, “2 is even and –3 is negative”?	a 2 is even and –3 is not negative.	b. 2 is odd and –3 is not negative.	c. 2 is even or –3 is not negative.	d. 2 is odd or –3 is not negative.	d
2235153	A partial ordered relation is transitive, reflexive and	a antisymmetric. 	b. bisymmetric.	c. antireflexive.	d. asymmetric.	a
2236155	 p      q is logically equivalent to	a. ~ q            p 	b. ~ p               q	c.~ p ^ q 	d. ~ p V q	d
2237156	In the following graph                                          the Euler path is	a. abcdef 	b. abcf	c. fdceab  	d. fdeabc	C 
2238157	The statement ( p^q)          p is a	a. Contingency. 	b. Absurdity	c. Tautology 	d. None of the above	c
2239158	The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is	a. Reflexive.	 b. Transitive.	c. Symmetric. 	d. Asymmetric.	b
2240159	A partial order relation is reflexive, antisymmetric and	a. Transitive.	 b. Symmetric.	c. Bisymmetric. 	d. Asymmetric.	a
2241160	The number of distinct relations on a set of 3 elements is:	a. 8 	b. 9	c. 18 	d. 512	d
2242161	A graph in which all nodes are of equal degrees is known as:	a. Multigraph	b. Regular graph	c. Complete lattice 	d. non regular graph	b
2243162	Which of the following set is null set?	a. {0} 	b. { }	c. {f}	d. f	b
2244163	 Transitivity and irreflexive imply:	a. Symmetric 	b. Reflexive	c. Irreflexive 	d. Asymmetric	d
2245164	 In an undirected graph the number of nodes with odd degree must be	a. Zero 	b. Odd	c. Prime 	d. Even	d
2246165	 Find the number of relations from A = {cat, dog, rat} to B = {male , female}	a. 64 	b. 6	c. 32 	d. 15	a
2247166	 The number of functions from an m element set to an n element set is:	a. mn 	b. m + n	c. nm 	d. m * n	a
2248167	 Which of the following proposition is a tautology?	a. (p v q)          p	 b. p v (q         p)	c. p v (p         q) 	d. p        (p         q)	c
2249168	 A graph with one vertex and no edges is:	a. multigraph 	b. digraph	c. isolated graph 	d. trivial graph	d
2250169	If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is	a. {(3,3), (3,4), (3,5)}	b. {(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}	c. {(3,3), (3,5), (5,3), (5,5)}	d. {(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}	c
2251170	 A complete graph of n vertices should have __________ edges.	a. n-1 	b. n	c. n(n-1)/2 	d. n(n+1)/2	c
2252171	 Which one is the contrapositive of q          p ?	a. p         q 	b. ¬p            ¬q	c. ¬q             ¬p 	d. None of these	b
2253172	 A relation that is reflexive, anti-symmetric and transitive is a	a. function 	b. equivalence relation	c. partial order 	d. None of these	c
2254173	 A Euler graph is one in which	a. Only two vertices are of odd degree and rests are even	b. Only two vertices are of even degree and rests are odd	c. All the vertices are of odd degree	d. All the vertices are of even degree	d
2255177	 ------------ is an association between two objects.	a)      Function	b) Relation   	c) Proposition	 d) Quantifiers	b
2256178	   -------- is defined to be subset of AXB from a set A to.	a)      Relation 	b) Binary Relation 	c) Both a & b 	d) None	c
2257179	Consider X={1,2,3}; Y={8,9}and R ={(1,8),(2,8),(1,9),(3,9)}. The inverse of relation is 	a)       {(8,1),(8,2),(1,9),(9,3)}	b)     {(8,1),(8,2),(9,1),(9,3)}	c)      {(1,8),(8,2),(9,1),(9,3)}	d)     {(8,1),(2,8),(9,1),(9,3)}	b
2258180	      Consider X={2,3,6}; Y={8,9}and R ={(2,8),(2,9),(6,9),(3,9)}. The compliment of relation is 	a)      {(2,8),(3,8),(6,9),(6,9)} 	b)      {(2,9),(6,8),(3,8)}	c)      {(3,8),(2,9),(6,9),(3,9)}	d)     {(3,8),(6,8)}	d
2259181	         Consider A={1,2,3,4} and R={(1,1)(1,2),(1,4),(2,3),(2,4),(3,4)}. The domain of R is 	a)      {1,2,3}	b)      {1,2,3,4}	c)      {2,3,4}	d)     None  	a
2260182	         Consider A={1,2,3,4} and R={(1,1)(1,2),(1,4),(2,3),(2,4),(3,4)}. The Range of R is 	a)      {1,2,3}	b)      {1,2,3,4}	c)      {2,3,4}	d)     None  	b
2261183	     Let N = {1, 2, 3, ….} be ordered by divisibility, which of the following subset is totally ordered, 	a. (2, 6, 24) 	b. (3, 5, 15) 	c. (2, 9, 16) 	d. (4, 15, 30)	a
2262184	   A relation R is called ---------if for every elements a€A, aRA.	a)      Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	d
2263185	      A relation R is called ---------if for every elements a€A, aRA, i.e (a,a)¢R	a) Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	a
2264186	        A relation R is called ---------if for every elements (a,b)€A implies (b,a)€R.	        a) Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	b
2265187	      A relation R is called ---------if for every elements (a,b), implies (b,a)¢R.	       a) Irreflexive	b) Symmetric  	c) Asymmetric 	d) Reflexive	c
2266188	      A relation R is called ---------if for every elements (a,b)€R and (b,a)€R the a=b.	       a) Antisymmetric	b) Symmetric  	c) Asymmetric 	d) Reflexive	a
2267189	          A relation R is called ---------if (a,b)€R and (b,c)€R then aRc.	       a) Antisymmetric	b) Symmetric  	c) Asymmetric 	d) Transitive	d
2268190	     Let A={1,2,3,4} and R ={(1,1),(2,2),(3,3)}. Is Relation is  	a)      Symmetric and Transitive 	b)      Reflexive and Antisymmetric	c)      Symmetric and Asymmetric  	d)     None 	a
2269191	         A Relation R on set A is called equivalence if it is 	a)      Reflexive	b) Transitive  	c) Symmetric 	d) All 	d
2270192	      An equivalence class of an element a is denoted with  	a)      [a]	b) (a)	c) {a}	d) None 	a
2271193	           Let R be a symmetric and transitive relation on set A. Then?	a)      R is reflexive and hence a partial order 	b)      R is reflexive and hence an equivalence relation 	c)      R is not reflexive and hence not an equivalence relation 	d)     None	d
2272194	     Find the domain for the relation: {(1,2), (5,3), (3,6),(2,4)}	A) {1,2,3,5}	B) {2,3,4,6}	c. {1,2,3,6}	d.{2,3,5,6}	a
2273195	        Find the range for the relation:{(3,5), (2,5), (2,6),(3,7)}	A) {5,6,7}	B) {2,3}	c. {1,2,3,6}	d.{2,3,5,6}	a
2274196	       If A and B are two non empty sets then Cartesian product of A and B is -------------	a)      AXB ={(a,b);a,b€A)}	b)      AXB ={(a,b);a,b€B)}	c)      AXB ={(a,b);a€A and b€B) }	d)     AXB ={(a,b);a€B and b€A) }	d
2275197	       If set A contains n elements, set B contains m elements then number of elements in AXB is –	a)      m+n	b) n-m	c) m.n	d) n/m 	c
2276198	       If A, B and C are non empty sets then AX(B∩C) is ------------	a)      ( AXB) U(AXC)	b)     ( AXB) ∩(AXC)	c)      ( AXB) ∩C	( AXC) ∩B	b
2277199	       If A, B and C are non empty sets then AX(BUC) is ------------	a)      ( AXB) U(AXC)	b)      ( AXB) ∩(AXC)	c)      ( AXB) UC	d)     ( AXC) UB	a
2278200	        If R is relation defined from set A to B then---------	a)      R=AXB	b)     R    AXB	c)      R     BXA 	d)     AXB         R	b
2279201	        If A,B and C are three sets and B         C then-------	a)      AXB=AXC	b)     AXB         AXC	c)      AXC              AXB	d)     None of these	b
2280202	     If A,B and C are three sets then(A-B)XC IS -------------	a)      (AXC)-(BXC) 	b)      (AXC)U(BXC) 	c)      (AXC)-(BXC) 	d)     None of these	a
2281203	   Find the domain of {(1,2),(2,3),(3,5),(4,5),(5,6)}. Is it a function?	A) {1,2,3,4,5}, yes	B) {1,2,3,4,5}, no	C) {2,3,5,6}, yes	D) {2,3,5,6}, no	a
2282204	       If R1 is relation from A to B and R2 is relation from B to C then----	a)      MR1. R2= MR1+ MR2	b)      MR1. R2= MR1- MR2	c)      MR1. R2= MR1. MR2	d)     None of these	c
2283205	   If R1 is relation from A to B and R2 is relation from B to C then------	a)      M(R1.R2)-1= MR1. MR2	b)      M(R1.R2)-1= MR1-1 . MR2-1	c)      M(R1.R2)-1= MR2-1. MR1-1	d)     None of these	c
2284206	If R1 and R2  are relations from A to B then --------	a)      (R1U R2 )-1   = R1-1U R2-1	b)      (R1U R2 )-1   = R2-1U R1-1	c)      (R1U R2 )-1   = R1-1∩ R2-1	d)     (R1U R2 )-1   = R2-1∩R1-1	d
2285207	     If R1 and R2  are relations from A to B then --------	a)      (R1∩ R2 )-1   = R1-1 ∩ R2-1	b)      (R1∩ R2 )-1   = R1-1U R2-1	c)      (R1∩ R2 )-1   = R2-1∩ R1-1	d)     (R1∩ R2 )-1   = R2-1 U R1-1	c
2286208	       If R1 and R2  are relations from A to B then R’ is compliment of R then  ------	a.       (R1∩ R2 )   = R1-1 ∩ R2-1	b.      (R1∩ R2 )   = R1-1U R2-1	c.       (R1∩ R2 )   = R2-1∩ R1-1	d.      (R1∩ R2 )   = R2-1 U R1-1	c
2287209	       A partial ordered relation is transitive, reflexive and 	a. Antisymmetric 	b. Bisymmetric 	c. Anti reflexive. 	d. Asymmetric 	a
2288210	       if R is set of real numbers and relation (<=(less than or equal to ) is defined on R then ________	a)      R is an equivalence relation	b)      R is Partial order Relation 	c)      R is symmetric but neither reflexive not transitive 	d)     R is antisymmetric but neither reflexive nor transitive  	a
2289211	  If f is function from set A to set B then which is true ?	a)      A is known as domain set 	b)      A is known as codomain set	c)      A is known as range	d)     None of these	a
2290212	        If  f: A→B is a function and∀ b∈B ∋a∈A if f(a)=b then __________	a)  f is one to one	b)    f is many one	c)    f is onto	d)    f is into 	a
2291213	     which statement is true	a)      every function is relation  	b)      every relation is function	c)      both a & b	d)     none of these	a
2292214	       which statement is true	a)      relation can be of the type one to many 	b)      function can be of type one to many	c)       both a & b	d)     None of these	a
2293215	     if R is symmetric and transitive then it is called	a)      equivalence relation	b)     tolerance relation	c)      poset	d)     none of these	b
2294216	       equivalence class of an element is denoted with_____	a)      [ ]	b)      { }	c)      ( )	d)     None of these	a
2295217	   If f :A→B is a function and range of f=B then ?	a)      f is one to one	b)      f is one to many	c)      f is many to one	d)     f is onto	d
2296218	        if f:A→B is a function and ∀ b∈B ∋a∈A such that f(a)=b alsof(a1)=f(a2)=>a1=a2 then	a)  f is bijective	b)    f is surjective but not injective	c)    f is injective but not surjective	d)    none of these	a
2297219	        if f:A→B is a function and ∀ b∈B ∋a∈A such that f(a)=b alsof(a1)=f(a2)=>a1=a2 then	a)  f is invertible	b)    f is not invertible	c)    f is many to one onto	d)    none of these	a
2298220	     if A={x,y,z} B={a,b,c,d} and f,g,h,s and t are correspondence defined from A to B such that  f={(x,a),(y,b),(z,c)} g={(x,a),(y,b),(z,c),(x,d)} for f and g, which statement is true?	a)      Both f and g are functions from A to B	b)     f is function from A to  but g is not function	c)      f is not function but g is function from A to B	d)     both f and g are not functions	b
2299221	1        if A={x,y,z} B={a,b,c,d} and f,g,h,s and t are correspondence defined from A to B such that  f={(x,a),(y,b),(z,c)} then for f which statement is  true?	a)      f is one to one	b)     f is one one into	c)      f is many one onto	d)     f is many one into	b
2300222	2          if A={x,y,z} B={a,b,c,d} and f,g,h,s and t are correspondence defined from A to B such that  g={(x,a),(y,a),(z,b)} for  g, which statement is true?	a)      g is one to one	b)     g is into	c)      g is many one into	d)     g is many one 	b
2301223	1        if f:A→B is a function then f-1    exists if only if _________	a)      f is many to one onto	b)      f is many to one into	c)      f is one to one onto	d)     f is one to one into	c
2302224	2        if f: A→B and g:B→C are two functions then composite of f and g is ______	a)      gof: A→C	b)      fog:A→C	c)      gof:C→A 	d)     fog:C→A	a
2303225	3        if f: A→B and g:C→D are two functions then fog will exist iff ______	a)      D=A	b)      B=C	c)      A=B	d)     C=D	a
2304226	1        If S={1,3,5,15,30} and aRb iff a|b then chains of S are _________	a)      {1,3,5,15}	b)      {1,3 15,30}	c)      {1,5,15,30}	d)     Both (b) and (c)	d
2305227	2        A lattice is a poset(A <=) in which every subset {a,b} of A has_______________	a)      A least upper bound	b)      A greatest lower bound	c)      Both a and b	d)     None of these	c
2306228	1           The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is 	Reflexive 	Transitive 	Symmetric 	Asymmetric	b
2307229	2        Find the number of relations from A = {cat, dog, rat} to B = {male , female} 	15	64	6	32	c
2308230	3        If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is 	{(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)} 	{(3,3), (3,4), (3,5)} 	{(3,3), (3,5), (5,3), (5,5)} 	{(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}	c
2309231	4            Let R = { ( 3, 3 ) ( 6, 6 ) ( ( 9, 9 ) ( 12, 12 ), ( 6, 12 ) ( 3, 9 ) ( 3, 12 ), ( 3, 6 ) } be a relation on the set A = { 3, 6, 9, 12 }. The relation is 	A.    Reflexive and transitive 	B.  Reflexive only 	C. An equivalence relation	D.  Reflexive and Symmetric only 	a
2310232	5        Let R = { ( 1, 3 ), ( 4, 2 ), ( 2, 4 ), ( 2, 3 ), ( 3, 1 ) } be a relation on the set A = { 1, 2, 3,4 }. The relation R is 	A.    a function 	B.  transitive 	C. not symmetric 	D. reflexive 	c
2311233	6        Evaluate f(x) = 3x - 5 for x = 2	A) f(2) = 27	B) f(2) = 1	C) f(2) = 4	D) none of these	b
2312234	7        Evaluate f(x) = 3x2 –x+ 5 for x = -2	A) f(-2) = 15	B) f(-2) = 19	C) f(-2) = 14	D) f(-2) = 20	b
2313235	8        Find the range for f(x) = -x2 + 3, given the domain {-3, 0, 4}	A) {12,-3,19}	B) {-6,3,-13}	C) {9,-3,-5}	D) {-12,-3,19}	a
2314236	9        Find the range for g(x) = x2 - 4x, given the domain {-2,1,3}	A) {12, -2, -3}	B) {12,-3,-3}	C) {6, -2, -3}	D) {6, 3, -3}	b
2315237	10    Find the range of the relation f(x) = 2x2, if the domain is {-2, -1, 0, 3, 4}	A) {8,2,0,18,32}	B) {-8, -2, 0,18,32}	C) {-4,-2,0,6,8}	D) None of these	a
2316238	11    Find the range of the relation f(x) = 2x2+1, if the domain is {2, 1, 0, -3, 4}	A) {9,3,1,19,33}	B) {-9,3,1,-19,33}	C) {9,3,0,19,32}	D)  {9,2,1,18,33}	a
2317239	1        Evaluate g(x) = 2x2 for x = -2	A) g(-2) = 8	B) g(-2) = -8	C) g(-2) = 4	D) none of these	a
2318240	2        if A={a,b,c} and R on A is defined by R={(a,b),(b,a),(a,a),(b,b)} then R is ________	a)      Reflexive and symmetric	b)      Antisymmetric and transitive	c)      Reflexive and transitive	d)      Symmetric and transitive	d
2319241	3          If A={1,2,3,4,5} and r on A is defined by R={(a,b); b-a=1} then ________	a)      R={(1,2),(2,3),(3,4),(4,5)}	b)      R={(2,1),(3,2),(4,3),(5,4)}	c)      R={(1,2),(2,3),(3,4),(4,5), (2,1),(3,2),(4,3),(5,4)}	d)     None of these	a
2320242	4        If A={1,2,3,4,5,6} and R on A is defined by R={(a,b); a-b=2x where x∈N, N is set of natural numbers} then ________	a)      R={(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}	b)     R={(3,1), (4,2), (5,3), (5,1), (6,4), (6,2)}	c)      R={(1,3), (3,1), (1,5), (5,1), (6,4), (4,6), (5,3), (3,5), (2,6), (6,2), (1,1), (2,2), (3,3), (4,4), (5,5), (6,6),}	d)     None of these	b
2321243	5        If S={(a,b); a,b ∈I } and (a,b) R (c,d) iff a+d=b+c then__________	a)      R is equivalence relation	b)      R is partial order relation	c)      R is reflexive , transitive but not symmetric 	d)     None of these	a
2322244	6         If N is theset of natural numbers and S={(a,b); a,b ∈N } and (a,b) R (c,d) iff ad=bc then__________	a)      R is equivalence relation	b)      R is partial order relation	c)      R is reflexive ,symmetric but not transitive 	d)     None of these	a
2323245	7        If I set of integers and R is a relation defined on set I. R={(a,b); a divides b or a|b} then ____	a)      R is reflexive but not transitive	b)      R is equivalence relation	c)      R is partial order relation	d)     R is reflexive, transitive but not antisymmetric	d
2324246	8         If A={2,3,5,6,10,15,30}  and aRb iff a|b then minimal elements of A are ______	a)      2	b) 3	c) 5 	d) All	d
2325247	9         If A={2,3,5,6,10,15,30}  and aRb iff a|b then maximal elements of A are ______	a)  15	b)10	c)30 	d) All	c
2326248	10     If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then upper bound of 2 & 3 are ______	a)  6	b)30	c) both (a) & (b) 	d) none of these	c
2327249	11    If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then lower bound of 2 & 3 are ______	a)  3	b) 5	c) 15 	d) all of these	a
2328250	12    If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then greatest lower bound of 30 & 45 are ______	a)  15	b)3	c) 5 	d) allof these	a
2329251	13    If A={2,3,5,6,10,15,30,45}  and aRb iff a|b then lower bound of 30 & 45 are ______	a)  15	b)3	c) 5 	d) allof these	d
2330252	14    If A={-2,-1,0,1,2} and f: A→R is defined by f(x)=x2  +1 where R is set of real numbers then __________	a)      f is one to one	b)      f is many to one onto	c)      f is many to one into	d)     f is one to one into	c
2331253	Which of the following statement is true:	Every graph is not its own sub graph.	The terminal vertex of a graph are of degree two.	A tree with n vertices has n edges.	A single vertex in graph G is a sub graph of G.	A single vertex in graph G is a sub graph of G.
2332254	A graph in which all nodes are of equal degrees is known as:	Multigraph	Regular graph	Complete lattice  	non regular graph	Regular graph
2333255	In an undirected graph the number of nodes with odd degree must be	Zero	Odd	Prime	Even	Even
2334256	The length of Hamiltonian Path in a connected graph of n vertices is	n-1	n	n+1	n/2	n-1
2335257	A graph with one vertex and no edges is	multigraph 	digraph 	isolated graph 	trivial graph	trivial graph
2336258	A complete graph of n vertices should have _____ edges.	n-1    	n	n(n-1)/2 	n(n+1)/2	n(n-1)/2 
2337259	A Euler graph is one in which	Only two vertices are of odd degree and rests are even	Only two vertices are of even degree and rests are odd	All the vertices are of odd degree	All the vertices are of even degree	All the vertices are of even degree
2338260	The maximum degree of any vertex in a simple graph with n vertex is	n-1	n+1	2n-1	n	n-1
2339261	The length of Hamiltonian Path in a connected graph of n vertices is	n-1	n	n+1	n/2	n-1
2340262	Let G1 & G2 are two graphs as shown 	Both G1 & G2 are Planer Graph	Both G1 & G2 are Non  Planer Graph	G1 is planer graph but G2 is non planer Graph.	 G1 is non planer graph but G2 is planer graph.	 G1 is non planer graph but G2 is planer graph.
2341263	For an undirected graph with n vertices and e edges, the sum of the degree of each vertex is equal to	2n                           (b)      (c)                      (d) 	(2n-1)/2                   	2e      	 e2/2	2e      
2342264	Suppose v is an isolated vertex in a graph, then the degree of v is:	0	1	2	3	0
2343265	In an undirected graph the number of nodes with odd degree must be	0	odd	Prime	Even	odd
2344266	Which of the following statement is true:	Every graph is not its own subgraph	The terminal vertex of a graph is of degree two.	A tree with n vertices has n edges.	A single vertex in graph G is a subgraph of G.	A single vertex in graph G is a subgraph of G.
2345267	A graph with one vertex and no edges is:	Multigraph	Digraph	Isolated graph	Trivial graph	Isolated graph
2346268	A complete graph of n vertices should have ____ edges.	n	n-1	n(n-1)/2 	n(n+1)/2 	n(n-1)/2 
2347269	A Euler graph is one in which	Only two vertices are of odd degree and rests are even	 Only two vertices are of even degree and rests are odd	All the vertices are of odd degree	All the vertices are of even degree	Only two vertices are of odd degree and rests are even
2348270	The length of Hamiltonian Path in a connected graph of n vertices is	N	N-1	N+1	N/2	N-1
2349271	The degree of any vertex of graph is	The number of edges incident with vertex	Number of vertex in a graph	Number of vertices adjacent to that vertex	Number of edges in a graph	Number of vertices adjacent to that vertex
2350272	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	None Of These	K Regular Graph
2351273	A graph with no edges is known as empty graph. Empty graph is also known as	Trivial graph	Regular graph	Bipartite graph	None of these	None of these
2352274	A graph G is called a ..... if it is a connected acyclic graph	Cyclic graph	Regular graph	Tree	Not a graph	Tree
2353275	The complete graph K, has... different spanning trees?	nn-2	n*n	nn	 n2	n*n
2354276	A spanning tree of a graph is one that includes	All the vertices of the graph	All the edges of the graph	Only the vertices of odd degree	Only the vertices of even degree	All the vertices of the graph
2355277	The number of distinct simple graphs with up to three nodes is	9	7	10	15	9
2356278	Consider the graph G where V(G)={A,B,C,D} and E(G)=[{A,B},{B,C},{C,D}]. The degree of each vertices A,B,C,D respectively in G are…..	1,2,3,2	1,3,2,2	 1,1,1,1	 1,2,2,3	 1,1,1,1
2357279	The minimum number of spanning trees in a connected graph with “n” nodes is	n-1	n/2	2	1	n-1
2358280	The Degree sequence of G is	2,2,3,3,4	 0,1,1,2,0	0,0,1,1,2	2,3,4	0,0,1,1,2
2359281	Let H be the plane drawing of the planer graph G. The Graph H has	10	11	6	None Of These	None Of These
2360282	The Graph G is Best Described as	Multigraph	A Pseudogarph	A Complete Graph	A Simple Graph	A Simple Graph
2361283	The graph g is not a regular graph because	Not all edges are of same length	It is a complete graph	It is a complete graph	Not all vertices have the same degree	Not all vertices have the same degree
2362284	The Maximum size of a simple graph of order 15 is	105	210	15	10	15
2363285	The size of complete bipartite graph K5,4	20	10	9	25	20
2364286	The size of a cyclic graph C5 is	25	5	10	15	10
2365287	Two Graphs are Isomorphic if	No. of edges in two graphs are equal	No. of vertices in two graphs are equal	Adjacency is maintained	All of the above	All of the above
2366288	A tree with n vertices has _____ edges	n	n+1	n-1	n-2	n-1
2367289	A binary Tree T has n leaf nodes. The number of nodes of degree 2 in T is:	log n	n	n-1	n+1	n
2368290	A spanning tree of a graph is one that includes	All the vertices of the graph	All the edges of the graph	Only the vertices of odd degree	Only the vertices of even degree	All the vertices of the graph
2369291	Which of the following statements is false ?	Every tree is a bipartite graph	A tree contains a cycle	A tree with n nodes contains n-1 edges	A tree is a connected graph	A tree with n nodes contains n-1 edges
2370292	A complete binary tree of level 5 has how many nodes?	15	25	63	30	25
2371293	The maximum number of nodes on level i of a binary tree is	2i-1	 3i-1	 i+1	2i+2	2i+2
2372294	What is the postfix form of the following prefix *+ab–cd	ab+cd–*	abc+*–	ab+*cd–	ab+*cd–	ab+cd–*
2373295	The maximum path length from the root to a leaf is a tree’s	Degree	Connectivity count	 Depth	Edge count	 Depth
2374296	A connected planer graph divides the plane into a number of regions. If the graph has 8 vertices and these are linked by 20 edges, then the number of regions is:	11	13	21	27	21
2375297	The nearest neighbor algorithm for solving the Traveling Salesman Problem is	An optimal and inefficient algorithm	An approximate and efficient algorithm	An approximate and inefficient algorithm	An optimal and efficient algorithm	An optimal and efficient algorithm
2376298	A tree is	any graph with one component.	any graph that is connected and has no circuits.	any graph that has no bridges.	any graph that has no circuits.	any graph that is connected and has no circuits.
2377299	The number of chords of tree of a connected graph G of v vertices and e edges is	v - 1	 e – v + 1	v + 1	e – v -1	 e – v + 1
2378300	A graph in which all nodes are of equal degrees is known as:	Multigraph	Regular graph	Complete lattice  	non regular graph	Regular graph
2379301	The prefix evolution of (a + b) * (c + d) is:	Ab + cd + *	*+ab +cd	+ab + cd + *	None of these	*+ab +cd
2380302	Evaluate the following prefix expression ++ 26 + - 1324	25	12	15	23	15