Tamil Nadu Open University (TNOU) 2008-2nd Sem M.C.A 1st year / " Computer Oriented Numerical Methods" 648 - Question Paper

MCA-648    MCA-08

M.C.A. DEGREE EXAMINATION - JUNE 2008.

First Year/Second Semester

COMPUTER ORIENTED NUMERICAL METHODS

Maximum marks : 75

Answer for 5 marks questions should not exceed 2 pages.

Answer for 10/15 marks questions should not exceed

5 pages.

PART A (5 x 5 = 25 marks)

Answer any FIVE questions.

1.    Explain Secant method for solving non-linear equations.

2.    Derive the iterative formula to compute the square root of a positive number.

3.    Compare direct and iterative methods to solve the system of Linear Equations.

4.    Solve by Cramers rule :

x + 4 y = 5 2x - y = 1

5.    What is inverse interpolation? Explain.

6.    Explain the principle of least squares.

7.    Write the formula of R-K methods upto Fourth Order.

PART B (5 x 10 = 50 marks)

Answer any FIVE questions.

8.    Find a root of the equation x log₁₀ x = 1.2 by Newtons method.

9.    Find a root of the equation, by bisection method :

3x = cos x +1.

10. Solve the system of equations.

10x + y + z = 12 x +10 y + z = 12

x + y + 10z = 12 ,by Gauss Elimination Method.

11.    Solve by Gauss-Seidel method :

10x - 5y - 2z = 3 4x -10 y + 3z = -3 x + 6 y + 10z = -3.

12.    Using Lagrangels formula, fit a polynomial to the following data.

x -1 0 2 3 y -8 3 1 12

Hence find y (1).

r⁶ dx

13. Evaluate I-- by Simpsons 1/3 rule and

J 1 + x

3/8 rule.

14. Solve = ^y2 ^x2 for x = 0.2, 0.4 given y(0) = 1, dx y² + x

using R-K method of fourth order.

3    MCA-648

Attachment: tamil-nadu-open-university--tnou--2008-m-c-a--50140-1.pdf

Earning:   Approval pending.