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IGNOU UNIVERSITY MCA - III (SEM 5) DEC 2009 : Numerical and Statistical Computing

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I MCSE-004 I MCA (Revised) Term-End Examination December, 2009 MCSE-004 : NUMERICAL AND STATISTICAL COMPUTING Maximum Marks : 100 Time : 3 hours Note : Question number 1 is compulsory. Attempt any three from the rest. Use of calculator is allowed. 1. (a) Explain truncation error. Show that 2+6 a(b c) ab ac, where : a = .05555 El b =.4545 El c = .4535 El Use bisection Method to find a root of the equation x 3 4x 9 =0 8 Go upto 5 - iteration only. Use Gauss - Elimination method to solve the following system of equations : 8 x1 + x2 + x3 =3 4X 1 + 3X 2 + 4X 3 = 8 9x 1 + 3x 2 + 4x 3 = 7 MCSE-004 1 P.T.O. Evaluate f(15), Given the following table of values : x - f(x) - 8 10 20 30 40 50 46 66 81 93 101 Calculate the value of the integral, 8 5.2 f log x 4 dx by. Trapezoidal rule. Waddles' rule. *(Take h =0.2). 2. (a) Find a root (correct to three decimal place) of x 3 5x +3 =0 by Newton-Raphson method. Use Jacobi's method to solve the equation : 8 8 20x+y-2z=17 3x +20y z = 18 2x 3y +20z =25 Explain the bisection method. MCSE-004 2 4 3. (a) Given : 5+3 (x)=sin(x) f (0.1) = 0.09983, f (0.2) = 0.19867 Use method of Lagrange's interpolation to find f(0.16). Find error in f(0.16). Evaluate . dx Use Gauss-Legendre three 1+x 0 point formula. Explain initial value problem with an example. 8 4 6 4. (a) Evaluate 5[ 2 + sin (2 .J) ] dx using 10 simpsons' rule with 11 points. (b) Solve the initial value problem 10 u 1 = 2tu 2 with u(0) =1 and h= 0.2 on the interval [0,1]. Use Fourth order classical Runge Kutta method. 5. (a) A farmer buys a quantity of cabbage seeds from a company that claims that approximately 90% of the seeds will germinate if planted properly. If four seeds are planted, what is the probability that exactly two will germinate ? MCSE-004 3 8 P.T.O. (b) In a partially destroyed laboratory record of an analysis of correlation data, the following results only are legible. 8 Variance of x = 9 Regression equation : 8x 10y + 66 = 0 40x 18y 214 = 0 What are Mean value of x and y. Correlation coefficient between x and y. (iii) Standard deviation of y. (c) Suppose that the amount of time one spends in a bank to withdraw cash from an evening counter is exponentially distributed with mean ten minutes, that is X = 110. What is the probability that the customer will spend more than 15 minutes in the counter ? -o0o- MCSE-004 4 4

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Additional Info : Mca - III (sem 5) December 2009 Question Paper - Numerical and Statistical Computing (Revised Course)
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