# Mathematical Physics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 57 - 62 of 76

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## Question 57

Mathematical Physics
Covariant and Contravariant Tensor

Appeared in Year: 2008

### Question

MCQ▾

Under a certain rotation of coordinate axes, a rank – 1 tensor transforms according to the orthogonal transformation defined by the relations . Under the same rotation a rank – 2 tensor would transform such that –

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 58

Mathematical Physics

Appeared in Year: 2008

### Question

MCQ▾

For arbitrary matrices and , if , then is equal to –

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 59

Mathematical Physics
Residue Theorem and Applications

Appeared in Year: 2008

### Question

MCQ▾

If , where is the unit circle taken anticlockwise and is the principal branch of the Logarithm function, which one of the following is correct?

### Choices

Choice (4)Response

a.

b.

c.

is not defined since has a branch cut

d.

by residue theorem

## Question 60

Mathematical Physics

Appeared in Year: 2007

### Question

MCQ▾

The eigenvalues of matrix are and . The matrix is –

### Choices

Choice (4)Response

a.

Anti – Hermitian

b.

Anti – unitary

c.

Unitary

d.

Hermitian

## Question 61

Mathematical Physics

Appeared in Year: 2007

### Question

MCQ▾

The points, where the series solution of the Legendre differential equation will diverge, are located at –

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question 62

Mathematical Physics

Appeared in Year: 2008

### Question

MCQ▾

The set of all polynomials of a real variable of degree two or less and with real coefficients, constitutes a real linear vector space . For and , which one of the following constitutes an acceptable scalar product?

### Choices

Choice (4)Response

a.

b.

c.

d.

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