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COMPUTER SCIENCE SOLVED MCQS
Discrete Mathematics Solved MCQs
A graph G is called a ..... if it is a connected acyclic graph
Cyclic graph
Regular graph
Tree
Not a graph
_____________________________________________________________________________________
What is the probability of choosing correctly an unknown integer between 0 and 9 with 3 chances ?
963/1000
966/1000
968/1000
969/1000
_____________________________________________________________________________________
In an undirected graph the number of nodes with odd degree must be
Zero
Odd
Prime
Even
_____________________________________________________________________________________
A graph is a collection of
Row and columns
Vertices and edges
Equations
None of these
_____________________________________________________________________________________
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
_____________________________________________________________________________________
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
_____________________________________________________________________________________
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 ?
2n(n+1)/2 and 2n.3n(n–1)/2
3n(n–1)/2 and 2n(n–1)
2n(n+1)/2 and 3n(n–1)/2
2n(n+1)/2 and 2n(n–1)/2
_____________________________________________________________________________________
The number of colours required to properly colour the vertices of every planer graph is
2
3
4
5
_____________________________________________________________________________________
In how many ways can a president and vice president be chosen from a set of 30 candidates?
820
850
880
870
_____________________________________________________________________________________
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?
1/8
1
7
8
_____________________________________________________________________________________
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
_____________________________________________________________________________________
A minimal spanning tree of a graph G is
A spanning sub graph
A tree
Minimum weights
All of above
_____________________________________________________________________________________
The number of leaf nodes in a complete binary tree of depth d is
2d
2d–1+1
2d+1+1
2d+1
_____________________________________________________________________________________
A partial ordered relation is transitive, reflexive and
Antisymmetric
Bisymmetric
Anti reflexive.
Asymmetric
_____________________________________________________________________________________
In a graph if e=[u, v], Then u and v are called
Endpoints of e
Adjacent nodes
Neighbors
All of above
_____________________________________________________________________________________
In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities?
100
120
110
150
_____________________________________________________________________________________
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
_____________________________________________________________________________________
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
_____________________________________________________________________________________
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
_____________________________________________________________________________________
The expression a+a c is equivalent to
a
a+c
c
1
_____________________________________________________________________________________
A graph with one vertex and no edges is
multigraph
digraph
isolated graph
trivial graph
_____________________________________________________________________________________
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 colours required to properly color vertices of every planar graph is
2
3
4
5
_____________________________________________________________________________________
A
B
C
D
_____________________________________________________________________________________
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
_____________________________________________________________________________________
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
(i) and (ii)
(i) and (iii)
(i) and (iv)
(ii) and (iii)
_____________________________________________________________________________________
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 continuous non intersecting curve in the plane whose origin and terminus coincide
Planer
Jordan
Hamiltonian
All of these
_____________________________________________________________________________________
A graph with n vertices will definitely have a parallel edge or self loop of the total number of edges are
more than n
more than n+1
more than (n+1)/2
more than n(n-1)/2
_____________________________________________________________________________________
A debating team consists of 3 boys and 2 girls. Find the number of ways they can sit in a row?
120
24
720
12
_____________________________________________________________________________________
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.
_____________________________________________________________________________________
Which of the following pair is not congruent modulo 7?
10, 24
25, 56
-31, 11
-64, -15
_____________________________________________________________________________________
A
B
C
D
_____________________________________________________________________________________
The maximum degree of any vertex in a simple graph with n vertices is
n–1
n+1
2n–1
n
_____________________________________________________________________________________
The complete graph with four vertices has k edges where k is
3
4
5
6
_____________________________________________________________________________________
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
_____________________________________________________________________________________
How many onto (or surjective) functions are there from an n-element (n => 2) set to a 2-element set?
2n
2n - 1
2n - 2
2(2n – 2)
_____________________________________________________________________________________
Suppose v is an isolated vertex in a graph, then the degree of v is
0
1
2
3
_____________________________________________________________________________________
The number of nodes in a complete binary tree of height h (with roots at level 0) is equal to
20 + 21 + ….. 2h
20 + 21 + ….. 2h-1
20 + 21 + ….. 2h+1
21 + ….. 2h+1
_____________________________________________________________________________________
Hasse diagram are drawn
Partially ordered sets
Lattices
Boolean algebra
None of these
_____________________________________________________________________________________
In how many ways can 5 balls be chosen so that 2 are red and 3 are black
910
990
970
960
_____________________________________________________________________________________
Circle has ____________
No vertices
Only 1 vertex
8 vertices
None of these
_____________________________________________________________________________________
How many different words can be formed out of the letters of the word VARANASI?
64
120
40320
720
_____________________________________________________________________________________
The proposition ~qvp is equivalent to
p?q
q?p
p?q
p?q
_____________________________________________________________________________________
A graph is tree if and only if
Is planar
Contains a circuit
Is minimally
Is completely connected
_____________________________________________________________________________________
If B is a Boolean Algebra, then which of the following is true
B is a finite but not complemented lattice
B is a finite, complemented and distributive lattice
B is a finite, distributive but not complemented lattice
B is not distributive lattice
_____________________________________________________________________________________
Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded
faces in any embedding of G on the plane is equal to
3
4
5
6
_____________________________________________________________________________________
The number of distinguishable permutations of the letters in the word BANANA are,
60
36
20
10
_____________________________________________________________________________________
If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is
{(3,3), (3,4), (3,5)}
{(3,1), (5,1), (3,2), (5,2), (5,3), (5,4)}
{(3,3), (3,5), (5,3), (5,5)}
{(1,3), (1,5), (2,3), (2,5), (3,5), (4,5)}
_____________________________________________________________________________________