Discrete Mathematics Solved MCQs

A graph G is called a ..... if it is a connected acyclic graph ...

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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)}       _____________________________________________________________________________________