CSIR Physical Sciences: Questions 40 - 43 of 401

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Question number: 40

» Mathematical Methods of Physics » Eigenvalues and Eigenvectors

Appeared in Year: 2014

MCQ▾

Question

The column vector (aba) is a simultaneous eigenvector of A=(001010100) and B=(011101110) if,

(December)

Choices

Choice (4) Response

a.

b=aorb=2a

b.

b=0ora=0

c.

b=a2orb=a2

d.

b=2aorb=a

Question number: 41

» Thermodynamic and Statistical Physics » Laws of Thermodynamics

Appeared in Year: 2014

MCQ▾

Question

The pressure P of a fluid is related to its number density ρ by the equation of state P=aρ+bρ2; where a and b are constants. If the initial volume of the fluid is V0, the work done on the system when it is compressed so as to increase the number density from an initial value of ρ0 to 2ρ0 is – (December)

Choices

Choice (4) Response

a.

(3a2+7ρ0b3)ρ0V0

b.

2ρ0V0

c.

(aln2+bρ0)ρ0V0

d.

(a+bρ0)ρ0V0

Question number: 42

» Mathematical Methods of Physics » Special Functions » Laguerre

Appeared in Year: 2011

MCQ▾

Question

The generating function,

F(x,t)=n=0Pn(x)tn

For the Legendre polynomials Pn(x) is F(x,t)=(12xt+t2)12 . The value of P3(1) is – (December)

Choices

Choice (4) Response

a.

52

b.

1

c.

+1

d.

32

Question number: 43

» Mathematical Methods of Physics » Matrices

Appeared in Year: 2012

MCQ▾

Question

A 2×2 matrix A has eigenvalues eiπ5 and eiπ6 . The smallest value of n such that An=I is – (December)

Choices

Choice (4) Response

a.

20

b.

60

c.

30

d.

120

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