Download GTU BE/B.Tech 2019 Summer 4th Sem New 2140505 Chemical Engineering Maths Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

SEMESTER-IV(NEW) — EXAMINATION - SUMMER 2019

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Subject Code:2140505 Date:09/05/2019

Subject Name: Chemical Engineering Maths

Time:02:30 PM TO 05:30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Define the following terms: 03

1. Accuracy
2. Precision

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3. Truncation Error

(b) Solve the following system of equations by Gauss Elimination 04 method:

2x+2y-2z=8, -4x-2y+2z=-14; -2x+3y+9z=9

(c) Explain diagonally dominant system. Use Gauss —Seidel method to 07 solve the system of equations up to three decimal places:

2x+15y+6z=72; 54x+y+z=110; -x+6y+27z=85

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Q.2 (a) Evaluate the sum v6 +v7 +v8 and find its percentage relative error. 03

(b) Find a real root of the equation x³ + x² — 1 = 0 using the bisection 04 method correct up to three decimal places.

(c) Discuss Newton-Raphson method geometrically. Find a real root of 07 the equation e^x —3x=0 up to two decimal places using Newton- Raphson method. Take x₀ =0.

OR

(c) Derive secant method. Find the root of the equation e^x —tanx =0 07 using the secant method correct up to three decimal places. Take x₁=1, x₀ =0.7.

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Q.3 (a) Write an algorithm for Newton-Raphson method. 03

(b) Find a real root of the equation x³ —9x +1 = 0 in the interval [2, 3] 04 by the regula falsi method.

(c) Discuss about the pitfalls of Gauss elimination method and 07 techniques for improvement.

OR

Q.3 (a) Prove that (i) ?=E-1, (ii) E=e^hD 03

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(b) Fit a straight line to the following data: 04

(c) Explain the principle of least squares and using it fit an exponential 07 curve y = ae^bx to the following data :

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Q.4 (a) Evaluate ?₀¹ 1/(1+x²) dx using trapezoidal rule with h =0.2. 03

(b) Using Newton’s backward difference interpolation formula find 04 f(0.40) from the following table:

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(c) Using Lagrange’s interpolation formula, find the interpolating 07 polynomial from the following table:

OR

Q.4 (a) Write an algorithm of Simpson’s 1/3 rule. 03

(b) Apply Euler’s method to solve the initial value problem dy/dx =y , where y(0) =1 over [0, 3] using step size 0.5. 04

(c) Write the formula for divided differences [x₀,x₁] and [x₀,x₁,x₂]. 07 Using Newton’s divided difference formula find f(9) from the following table:

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Q.5 (a) Define first, second and mixed boundary value problems for elliptic 03 equations.

(b) Find dy/dx at x =1.30 from the following data: 04

(c) Apply fourth order Runge-Kutta method to find approximate value 07 of y for x=0.2, in steps of 0.1;if dy/dx =x²+y², y(0) =1.

OR

Q.5 (a) Explain finite difference approximations to partial derivatives. 03

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(b) Determine whether the following partial differential equations are 04 elliptic, parabolic or hyperbolic:

1. ?²u/?x² +2 ?²u/?x?y + ?²u/?y² =0
2. 56 ?²u/?x² -2 ?²u/?x?y +4 ?²u/?y² = sin(3x+4y)

(c) Using Gauss Seidel method up to three iterations solve the Laplace 07 equation u_xx +u_yy =0 for the following square plate with boundary values as shown in the figure:

u=0

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u=100

u=100

u=100

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