379 + Mcqs in Discrete Mathematics Page 8 McqOptions

351.	In a graph if e=[u, v], Then u and v are called
A.	Endpoints of e
B.	Adjacent nodes
C.	Neighbors
D.	All of above
Answer» E.

Discussion

352.	A partial ordered relation is transitive, reflexive and
A.	Antisymmetric
B.	Bisymmetric
C.	Anti reflexive.
D.	Asymmetric
Answer» B. Bisymmetric

Discussion

353.	The number of leaf nodes in a complete binary tree of depth d is
A.	2d
B.	2d–1+1
C.	2d+1+1
D.	2d+1
Answer» B. 2d–1+1

Discussion

354.	A minimal spanning tree of a graph G is
A.	A spanning sub graph
B.	A tree
C.	Minimum weights
D.	All of above
Answer» E.

Discussion

355.	In a graph if e=(u, v) means
A.	u is adjacent to v but v is not adjacent to u
B.	e begins at u and ends at v
C.	u is processor and v is successor
D.	both b and c
Answer» E.

Discussion

356.	Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three?
A.	1/8
B.	1
C.	7
D.	8
Answer» D. 8

Discussion

357.	In how many ways can a president and vice president be chosen from a set of 30 candidates?
A.	820
B.	850
C.	880
D.	870
Answer» E.

Discussion

358.	The number of colours required to properly colour the vertices of every planer graph is
A.	2
B.	3
C.	4
D.	5
Answer» E.

Discussion

359.	How many relations are there on a set with n elements that are symmetric and a set with n elements that are reflexive and symmetric ?
A.	2n(n+1)/2 and 2n.3n(n–1)/2
B.	3n(n–1)/2 and 2n(n–1)
C.	2n(n+1)/2 and 3n(n–1)/2
D.	2n(n+1)/2 and 2n(n–1)/2
Answer» E.

Discussion

360.	An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are
A.	all of even degree
B.	all of odd degree
C.	of any degree
D.	even in number
Answer» B. all of odd degree

Discussion

361.	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
Answer» C. Symmetric

Discussion

362.	A graph is a collection of
A.	Row and columns
B.	Vertices and edges
C.	Equations
D.	None of these
Answer» C. Equations

Discussion

363.	In an undirected graph the number of nodes with odd degree must be
A.	Zero
B.	Odd
C.	Prime
D.	Even
Answer» E.

Discussion

364.	What is the probability of choosing correctly an unknown integer between 0 and 9 with 3 chances ?
A.	963/1000
B.	966/1000
C.	968/1000
D.	969/1000
Answer» B. 966/1000

Discussion

365.	A graph G is called a ..... if it is a connected acyclic graph
A.	Cyclic graph
B.	Regular graph
C.	Tree
D.	Not a graph
Answer» D. Not a graph

Discussion

366.	State True or False. Let f(x)=sin2(x) + log(x) then domain of f(x) is (-∞, ∞).
A.	True
B.	False
Answer» C.

Discussion

367.	If f(x) = x2 + 4 then range of f(x) is given by
A.	[4, ∞)
B.	(-∞, ∞) – {0}
C.	(0, ∞)
D.	None of the mentioned
Answer» B. (-∞, ∞) – {0}

Discussion

368.	If f(x) = 2x then range of the function is :
A.	(-∞, ∞)
B.	(-∞, ∞) – {0}
C.	(0, ∞)
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

369.	What is range of function f(x) = x-1 which is defined everywhere on its domain?
A.	(-∞, ∞)
B.	(-∞, ∞) – {0}
C.	[0, ∞)
D.	None of the mentioned
Answer» B. (-∞, ∞) – {0}

Discussion

370.	State whether the given statement is true or false Codomain is the subset of range.
A.	True
B.	False
Answer» C.

Discussion

371.	State whether the given statement is true or false The range of function f(x) = sin(x) is (-∞, ∞).
A.	True
B.	False
Answer» C.

Discussion

372.	What is domain of function f(x) = x-1 for it to be defined everywhere on domain?
A.	(2, ∞)
B.	(-∞, ∞) – {0}
C.	[0, ∞)
D.	None of the mentioned
Answer» C. [0, ∞)

Discussion

373.	Range of a function is :
A.	the maximal set of numbers for which a function is defined
B.	the maximal set of numbers which a function can take values
C.	it is set of natural numbers for which a function is defined
D.	none of the mentioned
Answer» C. it is set of natural numbers for which a function is defined

Discussion

374.	What is domain of function f(x)= x1/2 ?
A.	(2, ∞)
B.	(-∞, 1)
C.	[0, ∞)
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

375.	Domain of a function is :
A.	the maximal set of numbers for which a function is defined
B.	the maximal set of numbers which a function can take values
C.	it is set of natural numbers for which a function is defined
D.	none of the mentioned
Answer» B. the maximal set of numbers which a function can take values

Discussion

376.	What is the Cardinality of the Power set of the set {0, 1, 2}
A.	8
B.	6
C.	7
D.	9
Answer» B. 6

Discussion

377.	The Cartesian Product B x A is equal to the Cartesian product A x B. Is it True or
A.	True
B.	False
Answer» C.

Discussion

378.	The set O of odd positive integers less than 10 can be expressed by
A.	{1, 2, 3}
B.	{1, 3, 5, 7, 9}
C.	{1, 2, 5, 9}
D.	{1, 5, 7, 9, 11}
Answer» C. {1, 2, 5, 9}

Discussion

379.	A __________ is an ordered collection of objects.
A.	Relation
B.	Function
C.	Set
D.	Proposition
Answer» D. Proposition

Discussion

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