Mathematical Methods of Physics (CSIR Physical Sciences): Questions 30 - 32 of 67

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Question number: 30

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

Appeared in Year: 2012

MCQ▾

Question

Let y(x) be a continuous real function in the range 0 and 2π , satisfying the in homogeneous differential equation:

sinxd2ydx2+cosxdydx=δ(xπ2).

The value of dydx at the point x=π2 . (June)

Choices

Choice (4) Response

a.

Has a discontinuity of 13

b.

Is continuous

c.

Has a discontinuity of 1

d.

Has a discontinuity of 3

Question number: 31

» Mathematical Methods of Physics » Taylor & Laurent Series

Appeared in Year: 2014

MCQ▾

Question

The Laurent series expansion of the function f(z)=ez+e1z about z=0 is given by, (December)

Choices

Choice (4) Response

a.

n=znn!onlyif z <1

b.

n=0(zn+1zn)1n!forall0< z <

c.

n=znn!forall z <

d.

n=0(zn+1zn)1n!onlyif0< z <1

Question number: 32

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

Appeared in Year: 2014

MCQ▾

Question

The coordinates and momenta xi,pi(i=1, 2,3) of a particle satisfy the canonical Poisson bracket relation {xi,pj}=δij . If C1=x2p3+x3p2 and C2=x1p2x2p1 are constants of motion, and if C3={C1,C2}=x1p3+x3p1 , then – (June)

Choices

Choice (4) Response

a.

{C2,C3}=C1and{C3,C1}=C2

b.

{C2,C3}=C1and{C3,C1}=C2

c.

{C2,C3}=C1and{C3,C1}=C2

d.

{C2,C3}=C1and{C3,C1}=C2

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