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Posted By: santosh kumar kanugula Member Level: Gold Posted Date: 01 Jul 2008
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2007 Jawaharlal Nehru Technological University B.Tech Chemical engineering MATHEMATICS-II Question paper
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Code No: NR210101 NR
II B.Tech I Semester Supplementary Examinations, February 2007
MATHEMATICS-II
( Common to Civil Engineering, Electrical & Electronic Engineering,
Mechanical Engineering, Electronics & Communication Engineering,
Computer Science & Engineering, Chemical Engineering, Electronics &
Instrumentation Engineering, Bio-Medical Engineering, Information
Technology, Electronics & Control Engineering, Mechatronics, Computer
Science & Systems Engineering, Electronics & Telematics, Metallurgy &
Material Technology, Electronics & Computer Engineering, Production
Engineering and Aeronautical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Find the inverse of the matrix [8]
A =
2664
-1 -3 3 -1
1 1 -1 0
2 -5 2 -3
-1 1 0 1
3775
by using elementary row operations.
(b) Find whether the following equations are consistent, if so solve them. [8]
x1 + 2x2 + 3x3 = 16
x1 + x2 - 3x3 = -9
x1 - 2x2 + 2x3 = 8.
2. Diagnolize the matrix 24
-1 2 -2
1 2 1
-1 -1 0
35[16]
3. (a) If A= 24
2 3 + 2i -4
3 - 2i 5 6i
-4 -6i 3
35
show that A is Hermitian and iA is skew-
Hermitian matrices. [10]
(b) Prove that inverse of a unitary matrix is unitary.
(c) Prove that two eigen vectors of a symmetrix are orthogonal. [6]
4. (a) An alternating current after passing through rectifier has the form
i = I0sinx, for 0 x
0, for x 2
where I0 is the maximum current and the
period is 2. Express i as a Fourier series. [10]
(b) Represent the following function by Fourier sine series
f (x) = 1, 0 < x < m
2
0, m
2 < x < m
[6]
1 of 2
Code No: NR210101 NR
5. (a) Form the partial di erential equation by eliminating the arbitrary functions
z = f(x - it) + g( x - it) [5]
(b) Solve the partial di erential equation pyz + qz=xy . [5]
(c) Solve the partial di erential equation (z2 -2yz -y2)p+(xy +zx)q = xy -zx
[6]
6. If a string of length L is initially at rest in equilibrium position and each of its
points is given by the velocity (u/t)t=0 = bsin3(x/L) Find the displacement
y(x,t). [16]
7. Solve u
t = 2u
x2 for x > 0, t > 0, given that using Fourier transforms.
(a) u (0, t) = 0 for t > 0
(b) u (x, 0) = 1 for 0 < x < 1
0 for x 1
and
(c) u (x, t) is bounded. [16]
8. (a) Find Z[(n + 1)2] [6]
(b) Solve the di erence equation using z-transforms un+2-5un+1+6un = 4n given
that u0 = 0 u1 = 1. [10]
? ? ? ? ?
2 of 2
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