379 + Mcqs in Discrete Mathematics Page 7 McqOptions

301.	A product of the variables and their negations in a formula is called _________.
A.	elementary product
B.	elementary sum
C.	cnf
D.	dnf
Answer» B. elementary sum

Discussion

302.	Let p denote the statement: “Gopal is tall”, q: “Gopal is handsome”. Then the negation of the statement Gopal is tall, but not handsome,in symbolic form is:
A.	∼ p ˄q
B.	∼ p ˅ q
C.	∼ p ˅∼q
D.	∼ p ˄∼q
Answer» C. ∼ p ˅∼q

Discussion

303.	Each column of an incidence matrix of a graph G has exactly _______.
A.	one 1's
B.	two 1's
C.	one 2's
D.	two 2's
Answer» C. one 2's

Discussion

304.	A class of machine which accepts a ________ language is called finite state automata.
A.	type 0
B.	type 1
C.	type 2
D.	type 3
Answer» E.

Discussion

305.	A product of the variable and their negation in a formula is called ________.
A.	an elementary sum
B.	an elementary product
C.	a well-formed formula
D.	an equivalence of relation formula
Answer» C. a well-formed formula

Discussion

306.	The number of vertices of odd degree in a graph is always________.
A.	odd
B.	even
C.	zero
D.	one
Answer» C. zero

Discussion

307.	A minimal non-empty edge cut of G is called a _________.
A.	bond
B.	cycle
C.	path
D.	tour
Answer» B. cycle

Discussion

308.	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
Answer» B. G is bilaterally connected

Discussion

309.	If in the truth table the answer column has the truth values both TRUE and FALSE then itis said to be ________.
A.	tautology
B.	contradiction
C.	contingency
D.	equivalence relation
Answer» D. equivalence relation

Discussion

310.	A type-2 grammar contains the rules of the form is____.
A.	a tends to AB
B.	AaB tends to a
C.	A tends to aBC
D.	AB tends to CD
Answer» D. AB tends to CD

Discussion

311.	A __________ is a complemented distributive lattice.
A.	boolean homomorphism
B.	boolean algebra
C.	boolean isomorphism
D.	boolean function
Answer» E.

Discussion

312.	Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is
A.	7
B.	9
C.	10
D.	12
Answer» B. 9

Discussion

313.	Min-terms of two statements are formed by introducing the connective _________.
A.	Conjunction
B.	disjunction
C.	Conditional
D.	negation
Answer» B. disjunction

Discussion

314.	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
Answer» B. reflexive only

Discussion

315.	A sum of the variables and their negations in a formula is called _________.
A.	elementary sum
B.	elementary product
C.	cnf
D.	dnf
Answer» B. elementary product

Discussion

316.	The complement of the set A is _____________.
A.	a – b
B.	u – a
C.	a – u
D.	b – a
Answer» C. a – u

Discussion

317.	The specification of proper construction of a sentence is called ______.
A.	alphabet
B.	letter
C.	syntax
D.	word
Answer» D. word

Discussion

318.	Every non-trivial tree has at least _____ vertices of degree one.
A.	1
B.	2
C.	3
D.	4
Answer» C. 3

Discussion

319.	The contrapositive of p →q is
A.	~ q → ~ p
B.	~ p → ~ qc
C.	~ p → q
D.	~ q → p
Answer» B. ~ p → ~ qc

Discussion

320.	Let S be a start symbol and S -> aA, A -> BA, A -> a, B -> b be the productions in agrammar then one of the string derived form the grammar is _____.
A.	baba
B.	bbaa
C.	abba
D.	aabb
Answer» D. aabb

Discussion

321.	The number of subsets of a set containing n elements is
A.	n
B.	2n - 1
C.	n2
D.	2n
Answer» E.

Discussion

322.	If R= {(x, 2x)} and S= {(x, 4x)} then R composition S=____.
A.	{(x, 4x)}
B.	{(x, 2x)}
C.	{(x, 8x)}
D.	{(x, 10x)}
Answer» D. {(x, 10x)}

Discussion

323.	8. The set of positive integers is _________ .
A.	infinite
B.	finite
C.	subset
D.	empty
Answer» B. finite

Discussion

324.	The chromatic number of the chess board is ______.
A.	1
B.	2
C.	3
D.	4
Answer» C. 3

Discussion

325.	The statement from ∼ (p ˄ q) is logically equivalent to
A.	∼ p ˅ ∼ q
B.	∼ p ˅ qc
C.	p ˅ ∼ q
D.	∼ p ˄∼ q
Answer» B. ∼ p ˅ qc

Discussion

326.	Any vertex having degree one is called _______.
A.	Simple vertex
B.	pendent vertex
C.	regular vertex
D.	complete vertex
Answer» C. regular vertex

Discussion

327.	The relation R defined in A = {1, 2, 3} by aRb, if a2 – b2 £ 5. Which of the following is false?
A.	r = {(1, 1), (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)}
B.	r–1 = r
C.	domain of r = {1, 2, 3}
D.	range of r = {5}
Answer» E.

Discussion

328.	If A = { (1, 2, 3}, then the relation R = {(2, 3)} in A is
A.	symmetric and transitive only
B.	symmetric only
C.	transitive only
D.	not transitive
Answer» E.

Discussion

329.	R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R – 1 is
A.	{(11, 8), (13, 10)}
B.	{(8, 11), (10, 13)}
C.	{(8, 11), (9, 12), (10, 13)}
D.	none of the above
Answer» C. {(8, 11), (9, 12), (10, 13)}

Discussion

330.	A state from which a deterministic finite state automata can never come out is called a____________.
A.	trape state
B.	starting symbol
C.	transition table
D.	transition diagram
Answer» B. starting symbol

Discussion

331.	If A = {a,b,{a,c}, ∅}, then A - {a,c} is
A.	{a, b, ∅}
B.	{b, {a, c}, ∅}
C.	{c, {b, c}}
D.	{b, {a, c}, ∅}
Answer» B. {b, {a, c}, ∅}

Discussion

332.	Let X be a family of sets and R be a relation in X, defined by ‘A is disjoint from B’. Then, R is
A.	reflexive
B.	symmetric
C.	anti-symmetric
D.	transitive
Answer» C. anti-symmetric

Discussion

333.	A connected graph that has no cut vertices is called a ________.
A.	block
B.	bond
C.	cycle
D.	tour
Answer» B. bond

Discussion

334.	If r is a regular expression then r* is a _______ expression.
A.	regular
B.	irregular
C.	isomorphic
D.	homomorphic
Answer» B. irregular

Discussion

335.	If (∼ (p ˅ q)) → q is F, then
A.	p is t, q is f
B.	p is f, q is t
C.	p is t, q is t
D.	p is f, q is
Answer» C. p is t, q is t

Discussion

336.	Which of the following pair is not congruent modulo 7?
A.	10, 24
B.	25, 56
C.	-31, 11
D.	-64, -15
Answer» C. -31, 11

Discussion

337.	A debating team consists of 3 boys and 2 girls. Find the number of ways they can sit in a row?
A.	120
B.	24
C.	720
D.	12
Answer» B. 24

Discussion

338.	A graph with n vertices will definitely have a parallel edge or self loop of the total number of edges are
A.	more than n
B.	more than n+1
C.	more than (n+1)/2
D.	more than n(n-1)/2
Answer» E.

Discussion

339.	A continuous non intersecting curve in the plane whose origin and terminus coincide
A.	Planer
B.	Jordan
C.	Hamiltonian
D.	All of these
Answer» C. Hamiltonian

Discussion

340.	Choose the most appropriate definition of plane graph
A.	A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices
B.	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
C.	A simple graph which is Isomorphic to Hamiltonian graph
D.	None of these
Answer» B. 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

Discussion

341.	Which two of the following are equivalent for an undirected graph  G? (i) G is a tree (ii) There is at least one path between any two distinct vertices of G (iii) G contains no cycles and has (n-1) edges (iv)G has n edges
A.	(i) and (ii)
B.	(i) and (iii)
C.	(i) and (iv)
D.	(ii) and (iii)
Answer» C. (i) and (iv)

Discussion

342.	A graph with no edges is known as empty graph. Empty graph is also known as
A.	Trivial graph
B.	Regular graph
C.	Bipartite graph
D.	None of these
Answer» B. Regular graph

Discussion

343.	The number of colours required to properly color vertices of every planar graph is
A.	2
B.	3
C.	4
D.	5
Answer» B. 3

Discussion

344.	Length of the walk of a graph is
A.	The number of vertices in walk W
B.	The number of edges in walk W
C.	Total number of edges in a graph
D.	Total number of vertices in a graph
Answer» C. Total number of edges in a graph

Discussion

345.	A graph with one vertex and no edges is
A.	multigraph
B.	digraph
C.	isolated graph
D.	trivial graph
Answer» E.

Discussion

346.	The expression a+a c is equivalent to
A.	a
B.	a+c
C.	c
D.	1
Answer» C. c

Discussion

347.	In any undirected graph the sum of degrees of all the nodes
A.	Must be even
B.	Are twice the number of edges
C.	Must be odd
D.	Need not be even
Answer» C. Must be odd

Discussion

348.	A vertex of a graph is called even or odd depending upon
A.	Total number of edges in a graph is even or odd
B.	Total number of vertices in a graph is even or odd
C.	Its degree is even or odd
D.	None of these
Answer» D. None of these

Discussion

349.	A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are
A.	greater than n–1
B.	less than n(n–1)
C.	greater than n(n–1)/2
D.	less than n2/2
Answer» B. less than n(n–1)

Discussion

350.	In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities?
A.	100
B.	120
C.	110
D.	150
Answer» C. 110

Discussion

Explore topic-wise MCQs in VITEEE.

A product of the variables and their negations in a formula is called _________.

Let p denote the statement: “Gopal is tall”, q: “Gopal is handsome”. Then the negation of the statement Gopal is tall, but not handsome,in symbolic form is:

Each column of an incidence matrix of a graph G has exactly _______.

A class of machine which accepts a ________ language is called finite state automata.

A product of the variable and their negation in a formula is called ________.

The number of vertices of odd degree in a graph is always________.

A minimal non-empty edge cut of G is called a _________.

G is strongly connected implies _________.

If in the truth table the answer column has the truth values both TRUE and FALSE then itis said to be ________.

A type-2 grammar contains the rules of the form is____.

A __________ is a complemented distributive lattice.

Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is

Min-terms of two statements are formed by introducing the connective _________.

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 sum of the variables and their negations in a formula is called _________.

The complement of the set A is _____________.

The specification of proper construction of a sentence is called ______.

Every non-trivial tree has at least _____ vertices of degree one.

The contrapositive of p →q is

Let S be a start symbol and S -> aA, A -> BA, A -> a, B -> b be the productions in agrammar then one of the string derived form the grammar is _____.

The number of subsets of a set containing n elements is

If R= {(x, 2x)} and S= {(x, 4x)} then R composition S=____.

8. The set of positive integers is _________ .

The chromatic number of the chess board is ______.

The statement from ∼ (p ˄ q) is logically equivalent to

Any vertex having degree one is called _______.

The relation R defined in A = {1, 2, 3} by aRb, if a2 – b2 £ 5. Which of the following is false?

If A = { (1, 2, 3}, then the relation R = {(2, 3)} in A is

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R – 1 is

A state from which a deterministic finite state automata can never come out is called a____________.

If A = {a,b,{a,c}, ∅}, then A - {a,c} is

Let X be a family of sets and R be a relation in X, defined by ‘A is disjoint from B’. Then, R is

A connected graph that has no cut vertices is called a ________.

If r is a regular expression then r* is a _______ expression.

If (∼ (p ˅ q)) → q is F, then

Which&nbsp;of&nbsp;the&nbsp;following&nbsp;pair&nbsp;is&nbsp;not&nbsp;congruent&nbsp;modulo&nbsp;7?&nbsp;

A&nbsp;debating&nbsp;team&nbsp;consists&nbsp;of&nbsp;3&nbsp;boys&nbsp;and&nbsp;2&nbsp;girls.&nbsp;Find&nbsp;the&nbsp;number&nbsp;of&nbsp;ways&nbsp;they&nbsp;can&nbsp;sit&nbsp;in&nbsp;a&nbsp;row?

A&nbsp;graph&nbsp;with&nbsp;n&nbsp;vertices&nbsp;will&nbsp;definitely&nbsp;have&nbsp;a&nbsp;parallel&nbsp;edge&nbsp;or&nbsp;self&nbsp;loop&nbsp;of&nbsp;the&nbsp;total&nbsp;number&nbsp;of&nbsp;edges&nbsp;are&nbsp;

A&nbsp;continuous&nbsp;non&nbsp;intersecting&nbsp;curve&nbsp;in&nbsp;the&nbsp;plane&nbsp;whose&nbsp;origin&nbsp;and&nbsp;terminus&nbsp;coincide&nbsp;

Choose&nbsp;the&nbsp;most&nbsp;appropriate&nbsp;definition&nbsp;of&nbsp;plane&nbsp;graph&nbsp;

A&nbsp;graph&nbsp;with&nbsp;no&nbsp;edges&nbsp;is&nbsp;known&nbsp;as&nbsp;empty&nbsp;graph.&nbsp;Empty&nbsp;graph&nbsp;is&nbsp;also&nbsp;known&nbsp;as&nbsp;

The&nbsp;number&nbsp;of&nbsp;colours&nbsp;required&nbsp;to&nbsp;properly&nbsp;color&nbsp;vertices&nbsp;of&nbsp;every&nbsp;planar&nbsp;graph&nbsp;is&nbsp;

Length&nbsp;of&nbsp;the&nbsp;walk&nbsp;of&nbsp;a&nbsp;graph&nbsp;is

A&nbsp;graph&nbsp;with&nbsp;one&nbsp;vertex&nbsp;and&nbsp;no&nbsp;edges&nbsp;is&nbsp;

The&nbsp;expression&nbsp;a+a&nbsp;c&nbsp;is&nbsp;equivalent&nbsp;to&nbsp;

In&nbsp;any&nbsp;undirected&nbsp;graph&nbsp;the&nbsp;sum&nbsp;of&nbsp;degrees&nbsp;of&nbsp;all&nbsp;the&nbsp;nodes&nbsp;

A&nbsp;vertex&nbsp;of&nbsp;a&nbsp;graph&nbsp;is&nbsp;called&nbsp;even&nbsp;or&nbsp;odd&nbsp;depending&nbsp;upon&nbsp;

A&nbsp;graph&nbsp;with&nbsp;n&nbsp;vertices&nbsp;will&nbsp;definitely&nbsp;have&nbsp;a&nbsp;parallel&nbsp;edge&nbsp;or&nbsp;self&nbsp;loop&nbsp;if&nbsp;the&nbsp;total&nbsp;number&nbsp;of&nbsp;edges&nbsp;are&nbsp;

In&nbsp;how&nbsp;many&nbsp;ways&nbsp;can&nbsp;a&nbsp;hungry&nbsp;student&nbsp;choose&nbsp;3&nbsp;toppings&nbsp;for&nbsp;his&nbsp;prize&nbsp;from&nbsp;a&nbsp;list&nbsp;of&nbsp;10&nbsp;delicious&nbsp;possibilities?&nbsp;

Which of the following pair is not congruent modulo 7?

A debating team consists of 3 boys and 2 girls. Find the number of ways they can sit in a row?

A graph with n vertices will definitely have a parallel edge or self loop of the total number of edges are

A continuous non intersecting curve in the plane whose origin and terminus coincide

Choose the most appropriate definition of plane graph

A graph with no edges is known as empty graph. Empty graph is also known as

The number of colours required to properly color vertices of every planar graph is

Length of the walk of a graph is

A graph with one vertex and no edges is

The expression a+a c is equivalent to

In any undirected graph the sum of degrees of all the nodes

A vertex of a graph is called even or odd depending upon

A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are

In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities?