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GATE CS 2021 : Discrete Mathematics -11 (App update required to attempt this test)

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Question 1

In the word AKRISHNA, the total number of _____ circular permutation is possible.

Question 2

How many bit strings of length ten either start with a 1 bit or end with two bits 00?

Question 3

How many permutations of the word “CHANDRAYAN” is there?

Question 4

Calculate the number of ways of combination or selection of 11 players out of 20 players where A and B are always excluded.

Question 5

For a given graph G having v vertices and e edges which is connected and has no cycles, which of the following statements is true?

Question 6

Chromatic number of a star graph with n vertices (n>=2) is ___________.

Question 7

Which of the following is not true?

Question 8

Assume that ‘e’ is the number of edges and n is the number of vertices. The number of non-isomorphic graphs possible with n-vertices such that graph is 3-regular graph and e = 2n – 3 are .

Question 9

Consider the following Statements.

a) If G is a simple graph with n vertices (n>=3) such that every vertex degree in G is at least n/2 then G has a Hamiltonian cycle.

b) If G is a simple graph with n vertices with (n>=3) such that degree(u) + degree(v) >= n for every pair of non-adjacent vertices u and v in G, then G has a Hamiltonian cycle.

c) In a non-trivial tree there exist at least one vertex of degree

d) A complete Graph on 5 vertices is a planner graph.

Find the number of correct statements ____________?

Question 10

In the given graph identify the cut vertices.

Question 11

Let P: He is a great man, Q: You should not meet him.
Then ‘He is a great man and you should meet him.’ is best represented by?

Question 12

The set of intelligent students in a class is

Question 13

The number of multisets of size 4 are possible with the elements of the set S = {1, 2, 3, 4, 5, 6} is ________?

Question 14

Find the number of solutions of e1 + e2 + e3 = 17, where e1, e2, and e3 are nonnegative integers with 2 ≤ e1 ≤ 5, 3 ≤ e2 ≤ 6, and 4 ≤ e3 ≤ 7

Question 15

Let A, B and C be three sets, then(A-B)-C = _____
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