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Welcome to the Engineering Mathematics MCQs Page

Dive deep into the fascinating world of Engineering Mathematics with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Engineering Mathematics, a crucial aspect of GATE CSE Exam. In this section, you will encounter a diverse range of MCQs that cover various aspects of Engineering Mathematics, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within GATE CSE Exam.

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Check out the MCQs below to embark on an enriching journey through Engineering Mathematics. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of GATE CSE Exam.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Engineering Mathematics. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Engineering Mathematics MCQs | Page 22 of 23

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Q211.
The maximum number of edges in a bipartite graph of 12 vertices is __________________________.

a.

32

b.

30

c.

25

d.

36

Discuss
Answer: (d).36
Q212.
A cycle on n vertices is isomorphic to its complement. The value of n is _____.

a.

2

b.

4

c.

6

d.

5

Discuss
Answer: (d).5
Q213.
If G is a forest with n vertices and k connected components, how many edges does G have?

a.

floor(n/k)

b.

ceil(n/k)

c.

n-k

d.

n-k+1

Discuss
Answer: (c).n-k
Q214.
Let d denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with d ≥ 3, which one of the following is TRUE?

a.

In any planar embedding, the number of faces is at least n/2 + 2

b.

In any planar embedding, the number of faces is less than n/2 + 2

c.

There is a planar embedding in which the number of faces is less than n/2 + 2

d.

There is a planar embedding in which the number of faces is at most n/(d+1)

Discuss
Answer: (a).In any planar embedding, the number of faces is at least n/2 + 2
Q215.
The 2^n vertices of a graph G corresponds to all subsets of a set of size n, for n >= 6 . Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of vertices of degree zero in G is:

a.

1

b.

n

c.

n+1

d.

2^n

Discuss
Answer: (c).n+1
Q216.
The 2^n vertices of a graph G corresponds to all subsets of a set of size n, for n >= 6. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in G is:

a.

n

b.

n+2

c.

2^n/2

d.

2^n / n

Discuss
Answer: (b).n+2
Q217.
Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is

a.

6

b.

8

c.

9

d.

13

Discuss
Answer: (b).8
Q218.
Let G be a simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of G is 8. Then, the size of the maximum indepen­dent set of G is

a.

12

b.

8

c.

Less than 8

d.

More than 12

Discuss
Answer: (a).12
Q219.
Which one of the following graphs is NOT planar ?

a.

G1

b.

G2

c.

G3

d.

G4

Discuss
Answer: (a).G1
Q220.
Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?

a.

a path from s to t in the minimum weighted spanning tree

b.

a weighted shortest path from s to t

c.

an Euler walk from s to t

d.

a Hamiltonian path from s to t

Discuss
Answer: (a).a path from s to t in the minimum weighted spanning tree
Page 22 of 23

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