Download SGBAU BCA 2019 Summer 1st Sem Numerical Methods Question Paper

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B.C.A. (Part-1) Semester—I Examination

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NUMERICAL METHODS

Paper-1ST4

Time : Three Hours] [Maximum Marks : 60

Note :— (1) All questions are compulsory.

(2) All questions carry equal marks.

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(3) Assume suitable data wherever necessary.

1. (a) What do you mean by mathematical model ? How will you formulate it ? 4
   (b) What are the different phases involved in numerical computing ? 4
   (c) Distinguish between analog computing and digital computing. 4
   OR

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2. (a) Explain discrete data and continuous data involved in numerical computing with example. 4
   (b) Explain new trends in numerical computing. 4
   (c) What is Accuracy ? How is it affected during the process of Numerical computing ? 4
3. (a) Explain Inherent Errors. 4
   (b) Explain the concept of significant digit with proper example. 4
   

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   (c) Explain Round off errors. 4
   OR
4. (a) Round off the following numbers correct upto four decimal places :
   (i) 0.005789
   (ii) 0.235092
   

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   (iii) 56.243827
   (iv) 0.560012 4
   (b) Distinguish between rounding off error and truncation error. 4
   (c) What do you mean by significant digit ? Explain the term accuracy and precision related to significant digits. 4
5. (a) Describe how you will find out root of equation f(x) = 0 by Bisection method. 6
   

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   (b) Find graphically the positive root of an equation x² — 6x — 13=0 6
   OR
6. (a) Find the real root of equation f(x) = x³ — 3x — 5 = 0 by using false position method. 6
   (b) Find the root of equation f(x) = x³ — 4x — 9 = 0 by using Bisection method. 6
7. (a) State the Secant method formula for finding roots of an equation. 6
   

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   (b) Find the root of equation by using Secant method :
   f(x)=x²-4x-10=0 6
   OR
8. (a) Explain fixed point iteration method to find roots of non-linear equation. 6
   (b) Find the root of equation f(x) = x³ — x — 10 = 0 by using Newton-Raphson method. 6

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9. (a) Solve the following system of equation by using Gauss elimination with partial pivoting :
   x+y+z=1
   x+y-3z=5
   x-2y-5z=10 8
   (b) Write any four differences between Simple Gauss Elimination method and Gauss Jordan method. 4
   

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   OR
10. (a) Solve the following system of equation by using Gauss Jordan method :
    10x+2y +z=9
    x+ 10y — z=-22
    -2x + 3y + 10z = 22 8
    

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    (b) Explain the Gauss Elimination by partial pivoting method. 4

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