Jawaharlal Nehru Technological University Hyderabad 2010-1st Year B.Tech -\\Computer Science & Engineering\ regular\MATHEMATICAL METHODS set 3 - Question Paper

R09
SET-3
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-3

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, by reducing it to the normal form

b) Find whether the following system of equations are consistent. If so solve them.

x + y + 2z = 9, x - 2y + 2z = 3, 2x - y + z = 3, 3x - y + z = 4.    [8+7]

2. Verify Cayley Hamilton theorem and find the inverse of

3.    Reduce the quadratic form to the canonical form x² + y² + 2z² - 2xy + 4zx + 4yz [15]

4.a)    Find a real root of the equation e^x sin x=1using Newton Raphson method.

b) Find y(10), Given that y(5) = 12, y(6) = 13, y(9)=14, y(11) = 16 using Lagranges

formula.    [8+7]

5.a) Using the method of least squares find the constants a and b such that y = ae^bx fits the

x 0 0.5 1 1.5 2 2.5 y 0.10 0.45 2.15 9.15 40.35 180.75

b) Obtain a relation of the squares.

x	2	3	4	5	6
y	8.3	15.4	33.1	65.2	127.4

6.    Solve = xy +1 and y (0) = 1 using Taylors series method and compute y(0.1). [15]

dx

7.a)    If f(x)=cosh ax expand f(x) as a Fourier Series in (-n, n).

b) Expand the Function f(x) = x³ as a Fourier Series in -n < x < n .    [7+8]

8.    a) Solve (z²-2yz-y²)p + (xy + zx)q = xy - zx.

b) Find the integral surface of x (y² + z) p-y(x² + z) q = (x² + y²) z.    [7+8]

-oOo-

Attachment: jawaharlal-nehru-technological-university-hyderabad-2010-b-tech-43700-1.pdf

Earning:   Approval pending.