Engineering Mathematics [GATE (Graduate Aptitude Test in Engineering) Electronics]: Questions 18 - 27 of 71

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Question 18

Engineering Mathematics
Vector Space

Appeared in Year: 2016

Question

MCQ▾

Consider a square matrix

,

Where x is unknown. If the eigenvalues of the matrix A are and , then is equal to

Choices

Choice (4)Response

a.

b.

c.

d.

Question 19

Engineering Mathematics
Matrix Algebra

Appeared in Year: 2015

Question

MCQ▾

For the determinant of is

Choices

Choice (4)Response

a.

0

b.

1

c.

d.

Question 20

Engineering Mathematics
Taylor Series

Appeared in Year: 2015

Question

Numeric Answer▾

The value of is …

Question 21

Engineering Mathematics
Rank

Appeared in Year: 2017

Question

Numeric Answer▾

The rank of the matrix

Question 22

Engineering Mathematics
Cauchy's Integral Formula

Appeared in Year: 2016

Question

Numeric Answer▾

In the following integral, the contour C encloses the point and .

The value of the integral is …

Question 23

Engineering Mathematics
Matrix Algebra

Appeared in Year: 2019

Question

Numeric Answer▾

The number of distinct Eigen values of the matrix A = is equal to ________. (Carry One Mark Each)

Question 24

Engineering Mathematics
Analytic Functions

Appeared in Year: 2015

Question

Numeric Answer▾

Let If , for , then d should be equal to …

Question 25

Engineering Mathematics
Residue Theorem

Appeared in Year: 2017

Question

MCQ▾

The residues of function

Choices

Choice (4)Response

a.

b.

and

c.

and

d.

and

Question 26

Engineering Mathematics
Matrix Algebra

Appeared in Year: 2016

Question

MCQ▾

Let (where I denote the identity matrix) and , , . Then for any natural number k, equals:

Choices

Choice (4)Response

a.

b.

c.

d.

Question 27

Engineering Mathematics
Linear Dependence and Independence

Appeared in Year: 2017

Question

MCQ▾

Consider the following statements about the linear dependence of the real valued functions . Over the field of real numbers.

I. and are linearly independent on

II. and are linearly dependent on

III. and are linearly independent on

IV. and are linearly dependent on

Which one among the following is correct?

Choices

Choice (4)Response

a.

Both I and II are true

b.

Both II and IV are true

c.

Both III and IV are true

d.

Both I and III are true

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