Jawaharlal Nehru Technological University Kakinada 2009 B.Tech Computer Science Information Technology Mathematical methods SETNO 1, - Question Paper

Code No: Z0224/R07 Set No. 1
I B.Tech Supplementary Examinations, November 2009
MATHEMATICAL METHODS
( Common to Electrical & Electronic Engineering, Mechanical Engineering,
Electronics & Communication Engineering, Computer Science &
Engineering, Electronics & Instrumentation Engineering, Bio-Medical
Engineering, info Technology, Electronics & Control Engineering,
Mechatronics, Computer Science & Systems Engineering, Electronics &
Telematics, Electronics & Computer Engineering, Production Engineering,
Instrumentation & Control Engineering and Automobile Engineering)
Time: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks

1. (a) Express the subsequent system in matrix form and solve by Gauss elimination
method.
2x1 + x2 + 2x3 + x4 = 6; 6x1 - 6x2 + 6x3 + 12x4 = 36,
4x1 + 3x2 + 3x3 - 3x4 =- 1; 2x1 + 2x2 - x3 + x4 = 10.
(b) Show that the system of equations 3x + 3y + 2z = 1; x + 2y = 4;
10y + 3z = - 2; 2x - 3y - z = five is consistent and hence solve it. [8+8]

2. Determine the eigen values and the corresponding eigen vectors of the matrix A,
where A = [16]



one 0 -2
0 0 0
-2 0 4


3. decrease the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy to the canonical form and
specify the matrix of transformation. [16]

4. (a) obtain a positive root of the formula by bisection method: x3 - 4x - nine = 0
(b) obtain the positive root of x3 = 2x + five by False Position method. [8+8]

5. (a) It is known that x, y are related by y =a
x + bx and the experimental values
are provided below:
x: one two four six 8
y: 5.43 6.28 10.32 14.86 19.5
find the best values of a and b.
(b) obtain the 1st 2 derivatives of the function tabulated beneath at x=0.6
x: 0.4 0.5 0.6 0.7 0.8
y: 1.5836 1.7974 2.0442 2.3275 2.6511
[8+8]

6. obtain y(0.1), y(0.2), z(0.1), z(0.2) provided dy
dx = x + z, dz
dx = x - y2 and y(0) = 2, z(0)
= one by using Taylor's series method. [16]

7. (a) obtain the Fourier sine transform of e-ax cosx.
(b) obtain the Fourier cosine transform of x.e -ax. [8+8]

one of 2

Code No: Z0224/R07 Set No. 1


8. (a) Solve (x+y)p+(y+z)q=(z+x).
(b) Solve the difference equation, using Z-transform y(k+2)-2cos.y(k+1)+y(k)=0,
provided y(0)=1, y(1)= 1. [8+8]

two of 2

Earning:   Approval pending.