Mathematical Physics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 45 - 48 of 76

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Question 45

Mathematical Physics
Levi-Civita and Christoffel Symbols

Appeared in Year: 2009

Question

MCQ▾

Let and , where is the Levi – Civita density, defined to be zero if two of the indices coincide and and depending on whether is even or odd permutation of . Then is equal to –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 46

Mathematical Physics

Appeared in Year: 2009

Question

MCQ▾

The value of the contour integral, , for a circle of radius with centre at the origin is –

Choices

Choice (4)Response

a.

b.

c.

d.

Question 47

Mathematical Physics

Appeared in Year: 2009

Question

MCQ▾

Which one of the following curves given the solution of the differential equation , where and are positive constant with initial conditions and ?

Choices

Choice (4)Response

a.

The Curve, Solution of Diff. Equation: Choice A

b.

The Curve, Solution of Diff. Equation: Choice B

c.

The Curve, Solution of Diff. Equation: Choice C

d.

The Curve, Solution of Diff. Equation: Choice D

Question 48

Mathematical Physics

Appeared in Year: 2009

Question

MCQ▾

Consider the set of vectors in three – dimensional real vector space , . Which one of the following statement is true?

Choices

Choice (4)Response

a.

is a basis for

b.

An orthogonal set of vectors cannot be generated from

c.

The vectors in are orthogonal

d.

is not a linearly independent set

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