Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 4th Sem New 2140505 Chemical Engineering Maths Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2140505 Date: 07/12/2019
Subject Name: Chemical Engineering Maths
Time: 10:30 AM TO 01:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Define following,
1. Error 2. Truncation error 3. Relative error
03
(b) Evaluate the sum S = ?3 + ?5 + ?7 to 4 significant digits and find
its absolute and relative errors.
04
(c) Using the secant method, find a real root of equation
xe
x
? 1 = 0 correct to four decimal places.
07
Q.2 (a) Write an algorithm for Regula Falsi method. 03
(b) Evaluate ?12 correct to three decimal places using Newton-
Raphson method.
04
(c) Find root of the equation x
3
-
2x - 5 = 0 using the bisection method
correct upto three decimal places.
07
OR
(c) Use Gauss elimination method to solve the following system,
2x + y + z = 10, 3x + 2y + 3z = 18, x + 4y + 9z = 16
07
Q.3 (a) Define Eigen values and Eigen vectors. 03
(b) Describe Jacobi?s method. 04
(c) Solve the system, 6x + y + z = 20, x + 4y ? z = 6, x ? y + 5z = 7
using Gauss Seidel method.
07
OR
Q.3 (a) Find the inverse of the matrix,
1 2 3
A = 0 1 2
0 0 1
03
(b) Find the best values of a0 and a1 if the straight line
y = a0 + a1x is fitted to the data (xi, y i):
x 1 2 3 4 5
y 0.6 2.4 3.5 4.8 5.7
Find also the correlation coefficient.
04
(c) Find constants a and b such that the function y = ae
bx
fits the
following data:
x 1 3 5 7 9
y 2.473 6.722 18.274 49.673 135.026
07
Q.4 (a) Derive the formula for Simpson?s 3/8 Rule. 03
(b) Establish Newton?s forward interpolation formula. 04
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Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2140505 Date: 07/12/2019
Subject Name: Chemical Engineering Maths
Time: 10:30 AM TO 01:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Define following,
1. Error 2. Truncation error 3. Relative error
03
(b) Evaluate the sum S = ?3 + ?5 + ?7 to 4 significant digits and find
its absolute and relative errors.
04
(c) Using the secant method, find a real root of equation
xe
x
? 1 = 0 correct to four decimal places.
07
Q.2 (a) Write an algorithm for Regula Falsi method. 03
(b) Evaluate ?12 correct to three decimal places using Newton-
Raphson method.
04
(c) Find root of the equation x
3
-
2x - 5 = 0 using the bisection method
correct upto three decimal places.
07
OR
(c) Use Gauss elimination method to solve the following system,
2x + y + z = 10, 3x + 2y + 3z = 18, x + 4y + 9z = 16
07
Q.3 (a) Define Eigen values and Eigen vectors. 03
(b) Describe Jacobi?s method. 04
(c) Solve the system, 6x + y + z = 20, x + 4y ? z = 6, x ? y + 5z = 7
using Gauss Seidel method.
07
OR
Q.3 (a) Find the inverse of the matrix,
1 2 3
A = 0 1 2
0 0 1
03
(b) Find the best values of a0 and a1 if the straight line
y = a0 + a1x is fitted to the data (xi, y i):
x 1 2 3 4 5
y 0.6 2.4 3.5 4.8 5.7
Find also the correlation coefficient.
04
(c) Find constants a and b such that the function y = ae
bx
fits the
following data:
x 1 3 5 7 9
y 2.473 6.722 18.274 49.673 135.026
07
Q.4 (a) Derive the formula for Simpson?s 3/8 Rule. 03
(b) Establish Newton?s forward interpolation formula. 04
2
(c) Given the table of values as,
x 2.5 3.0 3.5 4.0 4.5
y(x) 9.75 12.45 15.70 19.52 23.75
Find y (4.25), using Newton?s backward difference interpolation
formula.
07
OR
Q.4 (a) Write an algorithm for Trapezoidal Rule. 03
(b)
Evaluate ?
????
1+?? 2
1
0
using Simpsons 3/8 rule taking
h =
1
6
.
04
(c)
Evaluate ? ?? 2
1
-0.5x
dx using four intervals for Simpson?s 1/3 rule
and Trapezoidal rule.
07
Q.5 (a) Describe the method of finite difference approximations to partial
derivatives.
03
(b) Use second order Runge ? Kutta method to solve
????
????
= 3x + y, given y = 1.3 when x = 1 to approximate y when x =
1.2 taking step size 0.1.
04
(c)
Determine the value of y at x=0.3, given that
????
????
= x + y and y(0)
=1, using modified Euler?s method.
07
OR
Q.5 (a) Discuss in brief about Milne?s Predictor-Corrector method. 03
(b) Using Taylor?s series method, obtain the solution of
????
????
= 3x + y
2
, given that y (0) = 1. Find the value of y for x = 0.1.
04
(c) Use fourth order Runge ? Kutta method to find the value of y when
x = 0.2, given that y? = x + y
2
, and y = 1 when x = 0 taking step size
0.1.
07
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This post was last modified on 20 February 2020