# Mathematical Physics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 15 - 20 of 76

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## Question 15

Mathematical Physics
Orthogonality and Completeness

Appeared in Year: 2012

### Question

MCQ▾

Identify the correct statement for the vectors and

### Choices

Choice (4)Response

a.

The vectors and are normalized

b.

The vectors and are orthogonal

c.

The vectors and are linearly independent

d.

The vectors and linearly dependent

## Question 16

Mathematical Physics
Residue Theorem and Applications

Appeared in Year: 2012

### Question

MCQ▾

The value of the integral , using the contour of circle with unit radius is –

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 17

Mathematical Physics
Cauchy-Riemann Conditions

Appeared in Year: 2012

### Question

MCQ▾

The number of independent component of the symmetric with indices is –

### Choices

Choice (4)Response

a.

9

b.

1

c.

3

d.

6

## Question 18

Mathematical Physics
Residue Theorem and Applications

Appeared in Year: 2013

### Write in Short

For the function , the residue at the pole is (your answer should be an integer) ________.

## Question 19

Mathematical Physics

Appeared in Year: 2013

### Question

MCQ▾

Which of the following pairs of the given function and its Laplace transform is NOT CORRECT?

### Choices

Choice (4)Response

a.

b.

c.

(Singularity at + 0)

d.

## Question 20

Mathematical Physics

Appeared in Year: 2011

### Question

MCQ▾

A matrix has elements such that its trace is and its determinant is . The eigenvalues of the matrix are all known to be positive integers. The largest eigenvalue of the matrix is –

### Choices

Choice (4)Response

a.

9

b.

12

c.

18

d.

6

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