Discrete Mathematics MCQs | Page - 9

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Q. From 1, 2, 3, …, 320 one number is selected at random. Find the probability that it is either a multiple of 7 or a multiple of 3.

(A) 72%
(B) 42.5%
(C) 12.8%
(D) 63.8%
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Q. If each and every vertex in G has degree at most 23 then G can have a vertex colouring of                      

(A) 24
(B) 23 c) 176
(C) d
(D) 54
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Q. Berge graph is similar to              due to strong perfect graph theorem.

(A) line graph
(B) perfect graph
(C) bar graph
(D) triangle free graph
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Q. A              is a graph which has the same number of edges as its complement must have number of vertices congruent to 4m or 4m modulo 4(for integral values of number of edges).

(A) subgraph
(B) hamiltonian graph
(C) euler graph
(D) self complementary graph
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Q. In a              the vertex set and the edge set are finite sets.

(A) finite graph
(B) bipartite graph
(C) infinite graph
(D) connected graph
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Q. If G is the forest with 54 vertices and 17 connected components, G has                total number of edges.

(A) 38
(B) 37
(C) 17/54 d
(D) 17/53
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Q. An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G?

(A) 1/2101
(B) 1/50 c) 1/100
(C) d
(D) 1/20
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Q. Triangle free graphs have the property of clique number is                      

(A) less than 2
(B) equal to 2
(C) greater than 3
(D) more than 10
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Q. Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?

(A) 4
(B) 0
(C) 2
(D) 5
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Q. A bridge can not be a part of                

(A) a simple cycle
(B) a tree
(C) a clique with size ≥ 3 whose every edge is a bridge
(D) a graph which contains cycles
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