Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 4th Sem New 2140505 Chemical Engineering Maths Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2140505 Date:22/11/2018
Subject Name:Chemical Engineering Maths
Time: 02:30 PM TO 05:30 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) Explain false position method. 03
(b) Differentiate between bracketing and open methods to solve non-linear algebraic
equations.
04
(c)
Find root of the equation
3
2 5 0 xx ? ? ? using bisection method.
07
Q.2 (a) Define: (1) Coefficient of determination, (2) Correlation coefficient, and (3)
standard error of estimate
03
(b) Explain Gauss elimination method with its pitfalls.
04
(c) Use Gauss-Jordan technique to solve the following three equations.
1 2 3
1 2 3
1 2 3
3 0.1 0.2 7.85
0.1 7 0.3 19.3
0.3 0.2 10 71.4
x x x
x x x
x x x
? ? ?
? ? ? ?
? ? ?
07
OR
(c)
Solve following equations using Newton-Raphson technique, starting with
? ?
T
0
x 0.5 0.5 ? . Carry out two iterations.
? ?
? ?
3
1 1 2 1 2 1
2
2 1 2 1 2 2
f x , x 4 8 x 4 x 2 x 0
f x , x 1 4 x 3x x 0
? ? ? ? ?
? ? ? ? ?
07
Q.3 (a) Given a value of 2.5 x ? with an error of 0.01 x ?? , estimate the resulting error
in the function, ? ?
3
f x x ?
03
(b) Explain the following terms with suitable example:
(1) Significant figures, (2) Relative error
04
(c) Use Jacobi?s method to solve the following three equations with initial values
1 2 3 4
0 x x x x ? ? ? ? . Carry out three iterations.
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
10 2 3
2 10 15
10 2 27
2 10 9
x x x x
x x x x
x x x x
x x x x
? ? ? ?
? ? ? ? ?
? ? ? ? ?
? ? ? ? ? ?
07
OR
Q.3 (a) Explain Gauss-Seidel method. 03
(b)
Suggest method to plot the variables y and x, given in the following equation, so that
data fitting the equation will fall on straight line.
? ?
x
y
1 x 1
?
?
? ? ?
04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2140505 Date:22/11/2018
Subject Name:Chemical Engineering Maths
Time: 02:30 PM TO 05:30 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) Explain false position method. 03
(b) Differentiate between bracketing and open methods to solve non-linear algebraic
equations.
04
(c)
Find root of the equation
3
2 5 0 xx ? ? ? using bisection method.
07
Q.2 (a) Define: (1) Coefficient of determination, (2) Correlation coefficient, and (3)
standard error of estimate
03
(b) Explain Gauss elimination method with its pitfalls.
04
(c) Use Gauss-Jordan technique to solve the following three equations.
1 2 3
1 2 3
1 2 3
3 0.1 0.2 7.85
0.1 7 0.3 19.3
0.3 0.2 10 71.4
x x x
x x x
x x x
? ? ?
? ? ? ?
? ? ?
07
OR
(c)
Solve following equations using Newton-Raphson technique, starting with
? ?
T
0
x 0.5 0.5 ? . Carry out two iterations.
? ?
? ?
3
1 1 2 1 2 1
2
2 1 2 1 2 2
f x , x 4 8 x 4 x 2 x 0
f x , x 1 4 x 3x x 0
? ? ? ? ?
? ? ? ? ?
07
Q.3 (a) Given a value of 2.5 x ? with an error of 0.01 x ?? , estimate the resulting error
in the function, ? ?
3
f x x ?
03
(b) Explain the following terms with suitable example:
(1) Significant figures, (2) Relative error
04
(c) Use Jacobi?s method to solve the following three equations with initial values
1 2 3 4
0 x x x x ? ? ? ? . Carry out three iterations.
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
10 2 3
2 10 15
10 2 27
2 10 9
x x x x
x x x x
x x x x
x x x x
? ? ? ?
? ? ? ? ?
? ? ? ? ?
? ? ? ? ? ?
07
OR
Q.3 (a) Explain Gauss-Seidel method. 03
(b)
Suggest method to plot the variables y and x, given in the following equation, so that
data fitting the equation will fall on straight line.
? ?
x
y
1 x 1
?
?
? ? ?
04
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2
(c)
Table below gives the temperatures (T) and length (L) of heated road. If
01
L a aT ?? , find the best values of a0 and a1 using linear regression.
T,
0
C 20 30 40 50 60 70
L, mm 800.3 800.4 800.6 800.7 800.9 801
07
Q.4 (a) Explain Simpson?s 3/8
th
rule.
03
(b) Explain Newton?s divided difference interpolation method.
04
(c)
Using Newton?s forward difference formula and data given in the table below, estimate
vapor pressure of ammonia vapor at 23?C. The latent heat of ammonia is 1265 kJ/kg.
Temperature, ?C 20 25 30 35
Pressure, kN/m
2
810 985 1170 1365
07
OR
Q.4 (a) From the following table of values of x and y , obtain dy/dx for x=1.2
x 1 1.2 1.4 1.6 1.8 2 2.2
Y 2.7183 3.3201 4.0552 4.9530 6.0496 7.3891 9.0250
07
(b)
Water is flowing through a pipe line 6 cm in diameter. The local velocities (u) at
various radial positions (r) are given below:
u, cm/s 2 1.94 1.78 1.5 1.11 0.61 0
r, cm 0 0.5 1 1.5 2 2.5 3
Estimate the average velocity u , using Simpson?s 1/3
rd
rule.
The average velocity is given by:
R
2
0
2
u u r dr
R
?
?
, where R is radius of pipe.
07
Q.5 (a) Explain Milne?s predictor corrector method.
03
(b) Explain procedure to solve following heat conduction equation using finite
difference technique.
2
2
TT
k
xt
??
?
??
04
(c)
Solve the following 3
rd
order ordinary differential equation using Euler method. At time,
t = 0, initial guess values are
0 0 0
1 2 3
x 2, x 16, x 4 ? ? ? . Use time interval from 0 to 1
second, with step size h = 0.5 sec.
32
32
d x d x dx
4 2 16 x 21
dt dt dt
? ? ? ?
07
OR
Q.5 (a)
Consider general linear 2
nd
order partial differential equation given below.
222
22
C C C C C
a b d e f gC h
r r z z r z
? ? ? ? ?
? ? ? ? ? ?
? ? ? ? ? ?
where, a, b, d, e, f, g and h are functions of r, z and their derivatives. How to check,
whether given partial differential equation is parabolic, hyperbolic or elliptic?
03
(b) Explain modified Euler?s method.
04
(c) Solve the following set differential equations using fourth order Runge-Kutta
method assuming that at x=0, y1=4 and y2=6. Integrate to x=1 with a step size of
0.5.
12
1 2 1
0.5 4 0.3 0.1
dy dy
y y y
dx dx
? ? ? ? ?
07
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This post was last modified on 20 February 2020