Mathematical Methods of Physics (CSIR Physical Sciences): Questions 25 - 29 of 67

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Question number: 25

» Mathematical Methods of Physics » Binomial, Poisson and Normal Distributions

Appeared in Year: 2014

MCQ▾

Question

If the electrostatic potential in spherical polar coordinates is φ(r)=φ0err0 ; where φ0 and r0 are constants, then the charge density at a distance r=r0 will be – (June)

Choices

Choice (4) Response

a.

ε0φ0er02

b.

eε0φ02r02

c.

ε0φ0er02

d.

2eε0φ0r02

Question number: 26

» Mathematical Methods of Physics » Linear Ordinary Differential Equations of First & Second Order

Appeared in Year: 2014

MCQ▾

Question

Consider the differential equation

d2xdt2+2dxdt+x=0

With the initial conditions x(0)=0 and x˙(0)=1 . The solution x(t) attains its maximum value when t is – (June)

Choices

Choice (4) Response

a.

12

b.

2

c.

1

d.

Question number: 27

» Mathematical Methods of Physics » Poles, Residues & Evaluation of Integrals

Appeared in Year: 2014

MCQ▾

Question

If C is the contour defined by z =12 , the value of the signal

Cdzsin2z

is – (June)

Choices

Choice (4) Response

a.

πi

b.

0

c.

d.

2πi

Question number: 28

» Mathematical Methods of Physics » Matrices

Appeared in Year: 2014

MCQ▾

Question

Consider the matrix M=(02i3i2i06i3i6i0) . The eigenvalues of M are – (June)

Choices

Choice (4) Response

a.

2,3,6

b.

5,2,7

c.

4i,2i,2i

d.

7,0,7

Question number: 29

» Mathematical Methods of Physics » Partial Differential Equations

Appeared in Year: 2012

MCQ▾

Question

The unit normal vector at the point,

(a3,b3,c3)

On the surface of the ellipsoid

x2a2+y2b2+z2c2=1, is – (December)

Choices

Choice (4) Response

a.

bci^+acj^+abk^b2c2+a2c2+a2b2

b.

ai^+bj^+ck^a2+b2+c2

c.

bi^+cj^+ak^a2+b2+c2

d.

bci^+caj^+abk^a2+b2+c2

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