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Code: 13A54102

B.Tech I Year (R13) Regular Examinations June/July 2014

MATHEMATICS - II

(Common to EEE, ECE, EIE, CSE & IT)

Time: 3 hours Max. Marks: 70

Part ? A

(Compulsory Question)

*****

1 Answer the following: (10 X 02 = 20 Marks)

(a) Find the Fourier constant bn for ? , when expressed as a Fourier series.

(b) Find the Fourier series defined in ?

(c) Find (x) = ?

(d) Write the complete solution of .

(e) Eliminate the arbitrary constants a and b from

(f) Find the rank of .

(g) Find the eigen values of the matrix .

(h) Write the condition for AX = B is consistent.

(i) Apply Euler?s method to solve find .

(j) Discuss the Netwon-Raphson method for convergence.

Part ? B

(Answer all five units, 05 X 10 = 50 Marks)

2

Using Cayley-Hamilton theorem, find the inverse of and also find .

OR

3 Reduce the quadratic form to the sum of squares form and find the

index and signature.

4 Using Newton?s forward interpolation formula, find the polynomial y = tan satisfying the following

data. Hence evaluate tan(0.12) and tan(0.28)

x 0.10 0.15 0.20 0.25 0.30

y 0.1003 0.1511 0.2027 0.2533 0.3093

OR

5

Dividing the range into 10 equal parts, find the value of . Using (i) Trapezoidal rule. (ii)

Simpson?s 1/3 rd rule.

6 Using Taylors series method with first five terms in the expansion find y(0.1) correct to three decimal

places, given that =

OR

7

Given . Is the function even or odd? Find the Fourier

series for f(x) and deduce the value of ???.

8

Find the Fourier sine transform of .

OR

9

Find: (i) (ii) .

10 Form partial differential equations by eliminating arbitrary constants.

(i) (ii) .

OR

11

Using the method of separation of variables, solve where U(x, 0)= .

R13

******

Unit - I

Unit - II

Unit - III

Unit - IV

Unit - V

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