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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 14 of 23

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Q131.
Consider the following matrix A. If the eigenvalues of A are 4 and 8, then

a.

x=4, y=10

b.

x=5, y=8

c.

x=-3, y=9

d.

x=-4, y=10

Discuss
Answer: (d).x=-4, y=10
Q132.
How many of the following matrices have an eigenvalue 1?

a.

one

b.

two

c.

three

d.

four

Discuss
Answer: (a).one
Q133.
If the matrix A is such that, then the determinant of A is equal to

a.

0

b.

1

c.

2

d.

3

Discuss
Answer: (a).0
Q134.
The product of the non-zero eigenvalues of the matrix

1 0 0 0 1
0 1 1 1 0
0 1 1 1 0
0 1 1 1 0
1 0 0 0 1

is ______

a.

4

b.

5

c.

6

d.

7

Discuss
Answer: (c).6
Q135.
Which one of the following statements is TRUE about every n×n matrix with only real eigenvalues?

a.

If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.

b.

If the trace of the matrix is positive, all its eigenvalues are positive.

c.

If the determinant of the matrix is positive, all its eigenvalues are positive.

d.

If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.

Discuss
Answer: (a).If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.
Q136.
Consider the set H of all 3 × 3 matrices of the following type, where a, b, c, d, e and f are real numbers and abc ≠ 0. Under the matrix multiplication operation, the set H is

a.

a group

b.

a monoid but not a group

c.

a semigroup but not a monoid

d.

neither a group nor a semigroup

Discuss
Answer: (a).a group
Q137.
Consider the following system of equations in three real variables x1, x2 and x3:

2x1 - x2 + 3x3 = 1
3x1- 2x2 + 5x3 = 2
-x1 + 4x2 + x3 = 3

This system of equations has

a.

no solution

b.

a unique solution

c.

more than one but a finite number of solutions

d.

an infinite number of solutions

Discuss
Answer: (b).a unique solution
Q138.
What are the eigenvalues of the following 2 × 2 matrix?

a.

-1 and 1

b.

1 and 6

c.

2 and 5

d.

4 and -1

Discuss
Answer: (b).1 and 6
Q139.
Let A, B, C, D be n × n matrices, each with non-­zero determinant. If ABCD = 1, then B^-1 is

a.

D^-1C^-1A^-1

b.

CDA

c.

ADC

d.

Does not necessarily exist

Discuss
Answer: (b).CDA
Q140.
In the LU decomposition of the matrix,

| 2 2 |
| 4 9 |

if the diagonal elements of U are both 1, then the lower diagonal entry l22 of L is

a.

4

b.

5

c.

6

d.

7

Discuss
Answer: (b).5
Page 14 of 23

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