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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