Jawaharlal Nehru Technological University Hyderabad 2010-1st Year B.Tech -\\Computer Science & Engineering\ regular\MATHEMATICAL METHODS set 2 - Question Paper
R09
SET-2
Code.No: 09A1BS04
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
I B.TECH – REGULAR EXAMINATIONS, JUNE - 2010
MATHEMATICAL METHODS
(COMMON TO EEE, ECE, CSE, EIE, BME, IT, ETE, E.COMP.E, ICE)
Time: 3hours Max.Marks:80
Code.No: 09A1BS04 R09 SET-2
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD I B.TECH - REGULAR EXAMINATIONS, JUNE - 2010 MATHEMATICAL METHODS (COMMON TO EEE, ECE, CSE, EIE, BME, IT, ETE, E.COMP.E, ICE) Time: 3hours Max.Marks:80
Answer any FIVE questions All questions carry equal marks
1.a) Find the Rank of the Matrix,
2 3 7
3 -2 4 1 -3 -1
by reducing it to the normal form.
b) Find all the non-trivial solutions of 2x - y + 3z = 0, 3x + 2y + z = 0, x - 4y + 5z = 0.
[7+8]
2. Find the eigen values and the corresponding eigen vectors of
1 3 7 1 2 3 1 2 1
[15]
1 + i 1 + i 1 + i 1 - i
b) Prove that the eigen values of a real skew symmetric matrix are either zero or purely imaginary.
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4.a) Find a real root of the equation 3x =ex by bisection method. b) Using Lagranges formula find y(6) given: | ||||||||||||
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5.a) Fit a straight line y = a + bx from the following data:
|
x |
0 |
1 |
2 |
3 |
4 |
|
y |
1 |
1.8 |
3.3 |
4.5 |
6.3 |
b) Fit a straight line to the form y = a + bx for the following data:
|
x |
0 |
5 |
10 |
15 |
20 |
25 |
|
y |
12 |
15 |
17 |
22 |
24 |
30 |
3. a) Prove that j
is unitary.
[8+7]
[7+8]
[7+8]
Find y(0.1), y(0.2),z(0.1), z(0.2) given = x + z, = x-y2 and y(0) = 2,
6.
dx dx
z (0) = 1by using Taylors series method.
[15]
7.a) Express f(x)=x as a Fourier Series in (-n, n).
b) Expand the function f(x) = x2 as a Fourier series in (-n, n)
8.a) Form the partial differential equation by eliminating a and b from log(az-l) = x + ay + b
b) Find the differential equation of all spheres whose centres lie on z-axis with a given radius r. [7+8]
-oOo-
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Attachment: |
| Earning: Approval pending. |
