Mathematical Methods of Physics (CSIR Physical Sciences): Questions 10 - 13 of 65

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Question number: 10

» 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: 11

» 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: 12

» 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

Question number: 13

» Mathematical Methods of Physics » Vector Algebra and Vector Calculus

Appeared in Year: 2014

MCQ▾

Question

Let r denote the position vector of any point in three dimensional space and r= r . Then, (December)

Choices

Choice (4) Response

a.

r=0and×r=rr

b.

r=3and2r=rr2

c.

r=3and×r=0

d.

r=0and2r=0

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