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Posted By: nihal Member Level: Gold Posted Date: 30 Jun 2008
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2007 Jawaharlal Nehru Technological University B.Tech mathematical methods Question paper
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Code No: R05010202 Set No. 2
I B.Tech Regular Examinations, Apr/May 2007
MATHEMATICAL METHODS
( Common to Electrical & Electronic Engineering, Electronics &
Communication Engineering, Computer Science & Engineering, Electronics
& Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Computer Science &
Systems Engineering, Electronics & Telematics, Electronics & Computer
Engineering and Instrumentation & Control Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Find a real root of the equation x3-x-11=0 by bisection method
(b) Construct difference table for the following data: [8+8]
x 0.1 0.3 0.5 0.7 0.9 1.1 1.3
F(x) 0.003 0.067 0.148 0.248 0.370 0.518 0.697
And find F(0.6) using a cube that fits at x=0.3, 0.5, 0.7 and 0.9 using Newton’s
forward formula.
2. (a) Derive normal equations to fit the straight line y=a+bx
(b) Evaluate
2
R0
e-x
2
dx using Simpson's rule.Taking h = 0.25. [8+8]
3. Given y' = x + sin y, y (0) = 1 compute y(0.2) and y(.4) with h=0.2 using Euler’s
modified method [16]
4. (a) Find whether the following equations are consistent, if so solve them.
x+y+2z = 4 ; 2x-y+3z= 9 ; 3x-y-z=2
(b) Find the rank of the matrix
????
1 2 3 0
2 4 3 2
3 2 1 3
6 8 7 5
????
by reducing it to the normal form. [8+8]
5. Diagomalize the matrix A = ?
?
1 1 1
0 2 1
-4 4 3
??
and hence find A4. [16]
6. (a) Define the following:
i. Hermitian matrix
ii. Skew-Hermitain matrix
iii. Unitary matrix
iv. Orthogonal matrix.
(b) Show that the eigen values of an unitary matrix is of unit modulus. [8+8]
7. (a) Find the Fourier series to represent f(x) = x2 - 2, when -2 _ x _ 2
(b) Show that the Fourier sine transform of
f(x) = ??
?
x for 0 < x < 1
2 - x for 1 < x < 2
0 for x > 2
is 2 sin s(1-cos s)
s
2 . [8+8]
8. (a) Form the partial differential equation by eliminating the arbitrary function
from z = yf(x2 + z2).
(b) Solve the partial differential equation ppx + qpy = pz
(c) Find Z-1 h 1
(z-5)3 i When |z| > 5. Determine the region of convergence.[5+5+6]
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