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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 21 of 23

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Q201.
Consider the following :

a.

K4 is planar while Q3 is not

b.

Both K4 and Q3 are planar

c.

Q3 is planar while K4 is not

d.

Neither K4 nor Q3 are planar

Discuss
Answer: (b).Both K4 and Q3 are planar
Q202.
Let G = (V,E) be a graph. Define ξ(G) = Σd id x d, where id is the number of vertices of degree d in G. If S and T are two different trees with ξ(S) = ξ(T),then

a.

|S| = 2|T|

b.

|S| = |T|-1

c.

|S| = |T|

d.

|S| = |T|+1

Discuss
Answer: (c).|S| = |T|
Q203.
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?

I. 7, 6, 5, 4, 4, 3, 2, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1

a.

I and II

b.

III and IV

c.

IV only

d.

II and IV

Discuss
Answer: (d).II and IV
Q204.
What is the chromatic number of an n-vertex simple connected graph which does not contain any odd length cycle? Assume n >= 2.

a.

2

b.

3

c.

n-1

d.

n

Discuss
Answer: (a).2
Q205.
Which of the following statements is true for every planar graph on n vertices?

a.

The graph is connected

b.

The graph is Eulerian

c.

The graph has a vertex-cover of size at most 3n/4

d.

The graph has an independent set of size at least n/3

Discuss
Answer: (c).The graph has a vertex-cover of size at most 3n/4
Q206.
Let G be the non-planar graph with the minimum possible number of edges. Then G has

a.

9 edges and 5 vertices

b.

9 edges and 6 vertices

c.

10 edges and 5 vertices

d.

10 edges and 6 vertices

Discuss
Answer: (c).10 edges and 5 vertices
Q207.
Which of the following graphs has an Eulerian circuit?

a.

Any k-regular graph where k is an even number

b.

A complete graph on 90 vertices

c.

The complement of a cycle on 25 vertices

d.

None of the above

Discuss
Answer: (c).The complement of a cycle on 25 vertices
Q208.
Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ?

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (b).B
Q209.
Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i, j): 1 <= i <= 12, 1 <= j <= 12}. There is an edge between (a, b) and (c, d) if |a − c| <= 1 and |b − d| <= 1. The number of edges in this graph is __________.

a.

500

b.

502

c.

506

d.

510

Discuss
Answer: (c).506
Q210.
An ordered n-tuple (d1, d2, … , dn) with d1 >= d2 >= ⋯ >= dn is called graphic if there exists a simple undirected graph with n vertices having degrees d1, d2, … , dn respectively. Which of the following 6-tuples is NOT graphic?

a.

(1, 1, 1, 1, 1, 1)

b.

(2, 2, 2, 2, 2, 2)

c.

(3, 3, 3, 1, 0, 0)

d.

(3, 2, 1, 1, 1, 0)

Discuss
Answer: (c).(3, 3, 3, 1, 0, 0)
Page 21 of 23

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