Download SGBAU BCA 2019 Summer 2nd Sem Numerial Methods Question Paper

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B.C.A. (Part—I) Semester—II Examination

2ST4 : NUMERICAL METHODS

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Time : Three Hours] [Maximum Marks : 60

Note :— (1) All questions are compulsory.

(2) All questions carry equal marks.

1. (a) What do you mean by Multiple Regression ? 4
   (b) Fit a straight line to the following data :
   

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   X 1 2 3 4 5
   Y 3 4 5 6 8
   (c) Show that regression coefficients are independent of change of origin but not of scale. 4
   OR
   (a) Derive normal equation for fitting of straight line.
   

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   (b) Explain regression.
   (c) Fit a multiple linear regression to the data given below :
   X₁ : 0 2 25 1 4 7
   X₂ 0 1 2 3 6 2
   Y : 10 9 0 3 27 4

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2. (a) Fit a power equation y = ax^b to the following given data :
   X 1 2 3 4 5
   y 0.5 1.7 3.4 5.7 8.4
   (b) Explain how you will reduce nonlinear equations in linear form.
   (c) Explain linear least square.
   

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   OR
3. (a) What do you mean by transcendental equation ?
   (b) Explain non-linear regression.
   (c) The population of a State at ten year interval is given below :
   Years 1925 1935 1945 1955 1965 1975 1985 1995
   

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   Population in millions 12.9 14.1 19.7 25.3 33.6 41.5 51.3 63.2
   Fit a curve of the form y = ab^x and estimate the population for the year 2005. 4
4. (a) State Newton Gregory forward interpolation formula. In which case is it useful ? 6
   (b) Using Lagrange’s interpolation formula compute f(5) from the given data :
   x : 2 4 7 9
   

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   f(x) : 10 26 65 101 6
   OR
5. (a) What do you mean by interpolation? Explain.
   (b) By means of Newton divided difference interpolation formula find the values of f(2) and f(8) from the following table :
   X 4 5 7 10 11 13
   

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   f(x) : 48 100 294 900 1210 2028
6. (a) Explain the inverse interpolation technique.
   (b) Explain the spline interpolation technique.
   (c) Using Lagrange’s inverse interpolation formula compute the value of x for y = 0.6742 :
   X 3.0 3.5 4.0 4.8 5.6
   

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   y 0.5441 0.6020 0.6812 0.7482 4
   OR
7. (a) What are assumptions of inverse interpolation ? 4
   (b) Explain the Chebyshev interpolation polynomial. 4
   (c) Using Lagrange’s interpolation formula estimate value of e^x using the following data :
   

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   X : 0 1 2 3
   e^x : 1 2.7183 7.3891 20.0855
8. (a) State and prove trapezoidal rule of numerical integration.
   (b) Evaluate ∫₁^1.4 1/x dx by using Simpson’s 1/3 rule. 6
   OR

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9. (a) State and prove Simpson’s 3/8 rule. 6
   (b) Solve using trapezoidal rule find the value of integral I = ∫₄^5.2 log x dx. 6

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