Mathematical Methods of Physics (CSIR Physical Sciences): Questions 55 - 57 of 65

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Question number: 55

» Mathematical Methods of Physics » Analytic Functions

Appeared in Year: 2012

MCQ▾

Question

A bag contains many balls, each with a number painted on it. There are exactly n balls which have the number n (namely one ball with 1, two balls with 2, and so on until N balls with N on them). An experiment consists of choosing a ball at random, nothing the number on it and returning it to the bag. If the experiment is repeated a large number of times, the average value of the number will tend to – (June)

Choices

Choice (4) Response
a.

N+12

b.

2N+13

c.

N(N+1)2

d.

N2

Question number: 56

» Mathematical Methods of Physics » Analytic Functions

Appeared in Year: 2011

MCQ▾

Question

Which of the following is an analytic function of the complex variable z=x+iy in the domain z <2 ? (June)

Choices

Choice (4) Response
a.

(3+xiy)7

b.

(1+x+iy)4(7xiy)3

c.

(12xiy)4(3xiy)3

d.

(x+iy1)12

Question number: 57

» Mathematical Methods of Physics » Fourier and Laplace Transforms

Appeared in Year: 2011

MCQ▾

Question

The graph of the function f(x)={1,for2nx2n+10,for2n+1x2n+2 (Where, n=0, 1,2 ) is shown below.

A graph of a periodic function

A Graph of a Periodic Function

In figure a graph of a periodic function is shown.

Its Laplace transform F¯(s) is – (December)

Choices

Choice (4) Response
a.

1ess

b.

1s(1es)

c.

1s(1+es)

d.

1ess

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