Download JNTUA B.Tech 1-1 R13 2014 Dec Supply 13A54102 Mathematics II Question Paper

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Code: 13A54102

B.Tech I Year (R13) Supplementary Examinations December/January 2014/2015
MATHEMATICS ? II
(Common to EEE, ECE, EIE, CSE and IT)
Time: 3 hours Max. Marks: 70
PART ? A
(Compulsory Question)

*****
1 Answer the following: (10 X 02 = 20 Marks)
(a) Find the sine series of .
(b) If then find
(c) Obtain the complete solution for
(d) Find .
(e) Find P. ? of (D2-2DD?) z = x
3
y.
(f) State one dimensional heat equation.

(g) Find the Eigen values for the matrix
(h) Write condition for the system AX = B is consistent.

(i) Find the rank of .
(j)
Using Euler?s method find the solution of the initial problem by assuming
h = 0.2.

PART ? B
(Answer all five units, 5 X 10 = 50 Marks)

UNIT - I

2 Reduce the quadratic form to the canonical form. Also specify the matrix
of transformation.
OR
3 State and prove Cayley-Hamilton theorem.

UNIT - II

4 Find the root of by Newton Raphson method corrected to three decimal places.
OR
5

Evaluate taking 4 intervals. Using (i) Trapezodial rule. (ii) Simpson?s 1/3 rd rule.

UNIT - III

6

Use fourth order Runge-Kutta method to compare y for x = 0.1, given
OR
7
Find the Half range Fourier sine series and hence deduce that:


UNIT - IV

8
Find the Fourier cosine transform of
OR
9

Solve Z-transform

UNIT - V

10
Solve the equation with boundary conditions where

OR
11 A tightly stretched string with fixed end points is initially in a position given by
if it is selected from rest from this position, find the displacement
*****
R13
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