Annamalai University 2008-2nd Year B.Sc Mathematics " 660 / 650 - II " ( PART - III - B - ANCILLARY ) ( ) 5246 - Question Paper

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8.    (a) Obtain a cosine series for e^-ax where

0 < X < oo.

(b) Obtain a sine series for unity in 0 < x < 71.

9.    Find:

L (t³ + 3t² - 6t + 8).

Find:

10. Using Laplace transform solve the differential equation

Name of the Candidate :

5 2 4 6 B.Sc. DEGREE EXAMINATION, 2008

(APPLIED CHEMISTRY/ELECTRONIC SCIENCE)

(SECOND YEAR)

(PART - III - B - ANCILLARY) 660/650. MATHEMATICS - II

(Including Lateral Entry )

December ]    [ Time : 3 Hours

Maximum : 75 Marks

Answer any FIVE questions.

All questions carry equal marks.

(5 x 15 = 75)

1. (a) Establish a reduction formula for

sinⁿx dx where n e N.

V r¹¹ r = (n + 3) r¹¹ where r = xi + yj + zk

and I r I

(b) Evaluate

F n ds

using Gauss divergence theorem for the function

F = 2xz i + yz j + z k over the upper half of the sphere

2 2 2 2 x + y + z = a .

3. (a) Solve:

P² + 2Py cot x = y².

(b) Solve:

(D² + 4D + 5)y = e^x + x² + cos 2x.

4. (a) Solve:

(x-a)P = P .

(b) Solve:

(D² - 4D + 13)y = e^2x cos 3x.

5.    (a) Solve:

pq + p + q = 0.

(b) Solve:

x = p + yzq = xy.

6.    (a) Solve:

y-z    z-x    x - y

- p + - q =-

yz        xy

(b) Solve:

p² - q² = 4.

7. Express

f(x) = Y (JE - X)

as Fourier series with period 271 to be valid in the interval 0 to 2k.

Deduce that

1 * * * + - ^K T ⁺ T T .....^- T

Turn over

Attachment: annamalai-university-2008-b-sc-mathematics-16688-1.pdf

Earning:   Approval pending.