Mathematical Methods of Physics (CSIR Physical Sciences): Questions 36 - 39 of 67

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Question number: 36

» Mathematical Methods of Physics » Special Functions » Bessel

Appeared in Year: 2014

MCQ▾

Question

The function f(x)=n=0(1)nn!(n+1)!(x2)2n+1 Satisfies the differential equation – (December)

Choices

Choice (4) Response

a.

x2d2fdx2+2xdfdx+(x21)f=0

b.

x2d2fdx2+xdfdx+(x21)f=0

c.

x2d2fdx2+xdfdx+(x2+1)f=0

d.

x2d2fdx2xdfdx+(x21)f=0

Question number: 37

» Mathematical Methods of Physics » Finite Difference Methods

Appeared in Year: 2011

MCQ▾

Question

Let, pn(x) (where, n = 0, 1, 2, …) be a polynomial of degree n with real coefficients, defined in the internal 2n4 . If

24pn(x)pm(x)dx=δnm,

then - (June)

Choices

Choice (4) Response

a.

p0(x)=12andp1(x)=32(3x)

b.

p0(x)=12andp1(x)=3(3+x)

c.

p0(x)=12andp1(x)=32(3x)

d.

p0(x)=12andp1(x)=32(3x)

Question number: 38

» Mathematical Methods of Physics » Eigenvalues and Eigenvectors

Appeared in Year: 2011

MCQ▾

Question

A 3×3 matrix M has Tr[M]=6,Tr[M2]=26,Tr[M3]=90 . Which of the following can be a possible set of eigenvalue of M? -

(December)

Choices

Choice (4) Response

a.

{1,1, 4}

b.

{1, 0,7}

c.

{1, 3,4}

d.

{2,2,2}

Question number: 39

» 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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