Download SGBAU B-Tech 6th Sem Chemical Engineering Computer Programming n Applications Question Paper

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B.Tech. Sixth Semester (Chemical Engineering) (CGS)

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10165 : Computer Programming & Applications : 6 CH 03/ 6 PP 03

Pages: 2 AW - 3248

Max. Marks : 80

Time : Three Hours

Notes : Answer Three question From Section "A" and Three question from Section "B".

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Due credit will be given to neatness and adequate dimensions.

Assume suitable data wherever necessary.

Use of pen Blue/Black ink/refill only for writing the answer book.

SECTION - A

1. a) Solve the following equation using Runge-Kutta second order and forth order formula. 10
   

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   dy/dx = y - x, y(0) = 2 Find y (0.1) & y (0.2) correct to four decimal places with h = 0.1
   b) Given dy/dx = 1 + xy. 4
   y (0) = 1, obtain the Taylor series for y (x) and compute y (0.1) correct to four decimal
   places.

OR

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1. a) Solve dy/dx = x²y using Euler's predictor corrector method with the initial condition
   y (0) = 1, find y (0.5) using a step size of h=0.1
   b) Derive Euler's predictor and corrector formula Also give difference between them. 6

1. a) Solve the following set of three linear equation in three variables using the Gauss- 7
   elimination method.
   

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   3x₁ + x₂ - 2x₃ = 9
   -x₁ + 4x₂ - 3x₃ = -8
   x₁ - x₂ + 4x₃ = 1
   b) Find the inverse of the matrix 6
   A =
   

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   1 -1 1
   1 -2 4
   1 2 2

OR

1. A liquid - liquid extraction process conducted in the Electrochemical material laboratory 13
   

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   involved the extraction of Nickel from aqueous phase into an organic phase. A set of
   experimental data is given bellow.
   Ni - aq. Phase, X(g/l) - 2 2.5 3
   Ni - organic phase, Y(g/l)- 8.57 10 12
   The Quadratic interpretation that estimate Y is given by Y = a₁x² + a₂x + a₃ 2 < x < 3.
   

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   The solution for constant a₁, a₂, a₃, is given by
   4 2 1 | a₁ | = | 8.57 | Find the value of a₁,
   6.25 2.5 1 | a₂ | = | 10 | a₂, a₃, by Gauss.
   9 3 1 | a₃ | = | 12 | Elimination method.
   Estimate the value at Y at x = 2.39 g/l

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1. a) Find the real root of the equation correct to three decimal places and between 0 and 0.5 for
   equation 4e^-xsinx -1 Using Regula Falsi method.
   b) Compute a real root from:
   f(x)= x³ -3x-5=0 using the Method of False Position.

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OR

1. a) Use Newton Raphson method to obtain a root correct to three decimal places of following
   equation. sin x = 1-x
   b) Use the method of false Position, to find out root of equation cos x- x e^x upto the four
   decimal place.

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SECTION - B

1. a) Economize the power series for the maximum error of 0.0005,
   Sinx = X - X³/3! + X⁵/5! - ...
   b) What do you mean by approximation of function? Explain in detail why we need to
   approximate a function? Which are the methods of approximation of function.

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OR

1. a) Find the values of a, b & c so that y = a + bx + cx² is the best fit to data
   X 0 1 2 3 4
   Y 1 0 3 10 21
   b) Estimate the criteria for the 'Best' fit for straight line.

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1. a) Minimize F(x₁,x₂) =(x₁-2)² +3(x₂ +3)² by the method of steepest descent using
   initial solution X⁰ = (1,-2)

OR

1. a) Explain
   i) Analytical method of optimization
   

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   ii) Gradient methods of optimization
   b) Explain Fibonacci search for n total number of experiment and uncertainty defined by
   as x < b

1. a) Explain in detail:
   1) Modular Programming
   

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   2) Subroutine libraries
   3) Capacity optimization

OR

1. a) Explain Block diagram of preliminary aids for programming.
   b) Describe how numerical method are implemented using subroutine libraries.

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