Tamil Nadu Open University (TNOU) 2009-2nd Year B.C.A Computer Application " COMPUTER ORIENTED NUMERICAL METHODS " UG 423 12 - Question Paper
UG-423 BCA-12
U.G. DEGREE EXAMINATION JANUARY, 2009.
(AY 2004-05 batch onwards)
Second Year
B.C.A.
COMPUTER ORIENTED NUMERICAL METHODS
Time : 3 hours Maximum marks : 75
Answer for 5 marks question should not exceed 2 pages.
Answer for 10 marks questions should not exceed 5 pages.
PART A (5 x 5 = 25 marks)
Answer any FIVE questions.
1. Find a real root of the equation x3 - 3x + 1 = 0 lying between 1 and 2 correct to three places of decimal by using Bisection method.
2. Define Interpolation, Extrapolation.
3. Define Errors in Numerical applications.
4. Explain Simpson's rule.
5. Explain Lagrange Interpolation method.
6. Discuss about System of Linear equations.
7. Explain the Iterative methods.
PART B (5 x 10 = 50 marks)
Answer any FIVE questions.
8. Solve 2x + y = 3, 2x + 3y = 5 by Gauss Seidal method.
9. (a) Solve the following system of simultaneous equations by Newton Raphson Method.
x2 + 3x - y = 0 xy + 3 y + 9 = 0
with x0 = -4, y0 = -6 .
(b) Derive Gauss Elimination method. dX
10. Evaluate I-- by using Trapezoidal and
0 1 + x
Simpson's rule.
11. (a) Use the method of iteration to fine the real root lying between 1 and 2 of the equation x3 - 3x + 1 = 0.
(b) Explain about Partial Pivoting.
12. (a) Explain Bisection method.
(b) Use Lagrange's interpolation formula to fit a polynomial to the data
X 0 1 3 4
Y - 0 6 1 : 12 2
Find the value of y when x = 2.
13. (a) Solve = 1 - y, y(0) = 0 using Euler's
dx
method. Find y at x = 0.1 and x = 0.2. Compare the result with results of the exact solution.
(b) Find by Regula-Falsi method, the positive root of x2 - log10 x - 12 = 0.
14. Fit a curve of the form y = axb + c to the following data using the group average method
|
X |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Y |
1 |
3 |
5 |
8 |
11 |
15 |
19 |
24 |
|
8 |
3 |
2 |
0 |
2 |
3 |
7 |
8 |
3 UG-423
|
Attachment: |
| Earning: Approval pending. |
