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TAMIL NADU OPEN UNIVERSITY MCA - I (SEM 2) JUN 2010 : Computer Oriented Num...

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WS 15 MCA 758 MCA-08 M.C.A. DEGREE EXAMINATION JUNE 2010. First Year COMPUTER ORIENTED NUMERICAL METHODS Time : 3 hours Maximum marks : 75 PART A (5 5 = 25 marks) Answer any FIVE questions. 1. Write about numbers and their accuracy. 2. Describe the method of false position. 3. Find, by Newton s method, the root of the equation ex 4x , which is approximately 2, correct to three decimal places. 4. Solve by Gauss-elimination method : 2x y 4z 12 8x 3y 2z 20 4x 11 y z 33. WS 15 5. Describe the Gauss-Jacobi method. 6. Given the data : x: 0 f (x) : 2 1 2 5 3 12 147 Find the cubic function of x . 7. dy 1 y with the initial dx condition x 0 , y 0 , using Euler s algorithm find the solution at x 0.1 and 0.2 . Solve the equation PART B (5 10 = 50 marks) Answer any FIVE questions. 8. Find the root of equation x 3 4x 9 0 correct to three decimal places by using the bisection method. 9. Show that the equation x 3 3x 1 0 has a root between 1 and 2. Calculate it to three decimal places using Horner s method. 10. Solve by Gauss-Jordon method : 5x 2 y 3z 18 x 7 y 3z 22 2x y 6z 22. 2 MCA 758 WS 15 11. Solve by Gauss-Seidel method of iteration : 27x 6x x 12. 6y 15 y y 2z 54 z 85 72 110 Compute f 0.9 by Newton-Gregory backward difference interpolation formula from the data : x: 0 0.2 0.4 0.6 0.8 1.0 f(x) : 13. z 1 1.16 3.56 13.96 41.96 101 Dividing the range into 10 equal parts, find the approximate value of sin x dx by 0 (a) (b) 14. Trapezoidal role and Simpson s 1/3 rule. Apply the fourth order Runge-Kutta method, to find an approximate value of y when x 0.2 and h 0.1 , given that y x y, y 0 1 . 3 MCA 758

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Additional Info : Mca - I (sem 2) June 2010 Question Paper - Computer Oriented Numerical Method
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