Mathematical Methods of Physics (CSIR Physical Sciences): Questions 58 - 62 of 67

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Question number: 58

» Mathematical Methods of Physics » Taylor & Laurent Series

Appeared in Year: 2011

MCQ▾

Question

The first few terms in the Taylor series expansion of the function f(x)=sinx around x=π4 are - (December)

Choices

Choice (4) Response

a.

12[1+(xπ4)+12!(xπ4)2+13!(xπ4)3+]

b.

12[1+(xπ4)12!(xπ4)213!(xπ4)3+]

c.

12[1x+x22!x33!]

d.

[(xπ4)13!(xπ4)3]

Question number: 59

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

Appeared in Year: 2011

MCQ▾

Question

Let x1(t) and x2(t) be two linearly independent solutions of the differential equation, d2xdt2+2dxdt+f(t)x=0 and let W(t)=x1(t)dx2(t)dtx2dx1(t)dt . If W(0)=1 , then W(1) is given by, (December)

Choices

Choice (4) Response

a.

1

b.

e-2

c.

1e

d.

1e2

Question number: 60

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

Appeared in Year: 2011

MCQ▾

Question

The value of the real integral I=3+3dxx2+3x+2 is – (December)

Choices

Choice (4) Response

a.

b.

ln(25)

c.

0

d.

3π2

Passage

Consider the matrix M=(111111111)

(June)

Question number: 61 (1 of 1 Based on Passage) Show Passage

» Mathematical Methods of Physics » Matrices

Appeared in Year: 2011

MCQ▾

Question

The eigenvalues of M are –

Choices

Choice (4) Response

a.

1, 1, 3

b.

0, 0,3

c.

1, 1,1

d.

0, 1,2

Passage

A resistance is measured by passing current through it and measuring the resulting voltage drop. If the voltmeter and the ammeter have uncertainties of 3% and 4% , respectively, then – (June)

Question number: 62 (1 of 2 Based on Passage) Show Passage

» Mathematical Methods of Physics » Dimensional Analysis

Appeared in Year: 2011

MCQ▾

Question

The uncertainty in the computed value of the power dissipated in resistance is:

Choices

Choice (4) Response

a.

9%

b.

7%

c.

5%

d.

11%

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