Mathematical Methods of Physics-Poles, Residues & Evaluation of Integrals (CSIR Physical Sciences): Questions 1 - 4 of 8

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Question number: 1

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

Appeared in Year: 2013

MCQ▾

Question

Given that the integral, 0dxy2+x2=π2y, the value of,

0dx(y2+x2)2is

(December)

Choices

Choice (4) Response

a.

π4y3

b.

π8y3

c.

πy3

d.

π2y3

Question number: 2

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

Appeared in Year: 2014

MCQ▾

Question

A time – dependent current I(t)=Ktz^; (where K is a constant) is switched on at t=0 in an infinite current – carrying wire. The magnetic vector potential is at a perpendicular distance ‘a’ from the wire. The magnetic vector potential at a perpendicular distance a from the wire is given (fortimet>ac) by – (June)

Choices

Choice (4) Response

a.

z^μ0K4πc2t2a2c2t2a2dzt(a2+z2)12

b.

z^μ0K4πCctctdz(cta2+z2)(a2+z2)12

c.

z^μ0K4πCc2t2a2c2t2a2dz(cta2+z2)(a2+z2)12

d.

z^μ0K4πctctdzt(a2+z2)12

Question number: 3

» 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: 4

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

Appeared in Year: 2014

MCQ▾

Question

The integral 01xdx is to be evaluated up to 3 decimal places using Simpson’s 3 – point rule. If the interval [0, 1] is divided into 4 equal parts, the correct result is – (June)

Choices

Choice (4) Response

a.

0.657

b.

0.638

c.

0.683

d.

0.667

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