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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 15 of 23

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Q141.
Consider the following 2 × 2 matrix A where two elements are unknown and are marked by a and b. The eigenvalues of this matrix are –1 and 7. What are the values of a and b?

A = | 1 4 |
| b a |

a.

a = 6, b = 4

b.

a = 4, b = 6

c.

a = 3, b = 5

d.

a = 5, b = 3

Discuss
Answer: (d).a = 5, b = 3
Q142.
The larger of the two eigenvalues of the matrix

⎡ 4 5 ⎤
⎣ 2 1 ⎦

is ____

a.

5

b.

6

c.

7

d.

8

Discuss
Answer: (b).6
Q143.
Perform the following operations on the matrix:

⎡ 3 4 45⎤
⎢ 7 8 105⎥
⎣13 2 195⎦

1. Add the third row to the second row.
2. Subtract the third column from the first column.

The determinant of the resultant matrix is _____________.

a.

0

b.

1

c.

50

d.

100

Discuss
Answer: (a).0
Q144.
In the given matrix, one of the eigenvalues is 1. the eigenvectors corresponding to the eigenvalue 1 are

⎡ 1 -1 2 ⎤
⎢ 0 1 0 ⎥
⎣ 1 2 1 ⎦

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (b).B
Q145.
If the following system has non-trivial solution,

px + qy + rz = 0
qx + ry + pz = 0
rx + py + qz = 0

then which one of the following options is True?

a.

p – q + r = 0 or p = q = –r

b.

p + q – r = 0 or p = –q = r

c.

p + q + r = 0 or p = q = r

d.

p – q + r = 0 or p = –q = –r

Discuss
Answer: (c).p + q + r = 0 or p = q = r
Q146.
Let a(x, y), b(x, y,) and c(x, y) be three statements with variables x and y chosen from some universe. Consider the following statement:

(∃x)(∀y)[(a(x, y) ∧ b(x, y)) ∧ ¬c(x, y)]

Which one of the following is its equivalent?  

a.

(∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]

b.

(∃x)(∀y)[(a(x, y) ∨ b(x, y)) ∧¬ c(x, y)]

c.

¬ (∀x)(∃y)[(a(x, y) ∧ b(x, y)) → c(x, y)]

d.

¬ (∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]

Discuss
Answer: (c).¬ (∀x)(∃y)[(a(x, y) ∧ b(x, y)) → c(x, y)]
Q147.
What values of x, y and z satisfy the following system of linear equations?

a.

x=6,y=3,z=2

b.

x=12,y=3,z=-4

c.

x=6,y=6,z=-4

d.

x=12,y=-3,z=0

Discuss
Answer: (c).x=6,y=6,z=-4
Q148.
Two eigenvalues of a 3 x 3 real matrix P are (2 + √ -1) and 3. The determinant of P is _____  

a.

0

b.

1

c.

15

d.

-1

Discuss
Answer: (c).15
Q149.
Let f (x) be a polynomial and g(x) = f (x) be its derivative. If the degree of (f(x) + f(−x)) is 10, then the degree of (g(x) − g(−x)) is _______________ .

a.

8

b.

7

c.

9

d.

10

Discuss
Answer: (c).9
Q150.
Consider the systems, each consisting of m linear equations in n variables.

I. If m < n, then all such systems have a solution
II. If m > n, then none of these systems has a solution
III. If m = n, then there exists a system which has a solution

Which one of the following is CORRECT?

a.

I, II and III are true

b.

Only II and III are true

c.

Only III is true

d.

None of them is true

Discuss
Answer: (c).Only III is true
Page 15 of 23

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