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

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 4th Sem New 2140505 Chemical Engineering Maths Previous Question Paper

1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV(NEW) ? EXAMINATION ? SUMMER 2019
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.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Define the following terms:
1. Accuracy
2. Precision
3. Truncation Error
03
(b) Solve the following system of equations by Gauss Elimination
method:
; 8 2 2 2 ? ? ? z y x ; 14 2 2 4 ? ? ? ? ? z y x 9 9 3 2 ? ? ? ? z y x
04
(c) Explain diagonally dominant system. Use Gauss ?Seidel method to
solve the system of equations up to three decimal places:
72 6 15 2 ? ? ? z y x ; 110 54 ? ? ? z y x ; 85 27 6 ? ? ? ? z y x
07

Q.2 (a)
Evaluate the sum 8 7 6 ? ? and find its percentage relative error.
03
(b) Find a real root of the equation ? 3
+ ? 2
? 1 = 0 using the bisection
method correct upto three decimal places.
04
(c) Discuss Newton-Raphson method geometrically. Find a real root of
the equation 0 3 ? ? x e
x
up to two decimal places using Newton-
Raphson method. Take . 0
0
? x
07
OR
(c)
Derive secant method. Find the root of the equation 0 tan ? ?
?
x e
x

using the secant method correct up to three decimal places. Take
7 . 0 , 1
1 0
? ? x x .
07
Q.3 (a) Write an algorithm for Newton-Raphson method. 03
(b)
Find a real root of the equation 0 1 9
3
? ? ? x x in the interval [2, 3]
by the regula falsi method.
04
(c) Discuss about the pitfalls of Gauss elimination method and
techniques for improvement.
07
OR
Q.3 (a)
Prove that (i) 1 ? ? ? E , (ii)
hD
e E ?
03
(b) Fit a straight line to the following data:
x 0 1 2 3 4
y 1 1.8 3.3 4.5 6.3

04
(c) Explain the principle of least squares and using it fit an exponential
curve
bx
ae y ? to the following data :
x 0 2 4 6 8
y 150 63 28 12 5.6

07










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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV(NEW) ? EXAMINATION ? SUMMER 2019
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.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Define the following terms:
1. Accuracy
2. Precision
3. Truncation Error
03
(b) Solve the following system of equations by Gauss Elimination
method:
; 8 2 2 2 ? ? ? z y x ; 14 2 2 4 ? ? ? ? ? z y x 9 9 3 2 ? ? ? ? z y x
04
(c) Explain diagonally dominant system. Use Gauss ?Seidel method to
solve the system of equations up to three decimal places:
72 6 15 2 ? ? ? z y x ; 110 54 ? ? ? z y x ; 85 27 6 ? ? ? ? z y x
07

Q.2 (a)
Evaluate the sum 8 7 6 ? ? and find its percentage relative error.
03
(b) Find a real root of the equation ? 3
+ ? 2
? 1 = 0 using the bisection
method correct upto three decimal places.
04
(c) Discuss Newton-Raphson method geometrically. Find a real root of
the equation 0 3 ? ? x e
x
up to two decimal places using Newton-
Raphson method. Take . 0
0
? x
07
OR
(c)
Derive secant method. Find the root of the equation 0 tan ? ?
?
x e
x

using the secant method correct up to three decimal places. Take
7 . 0 , 1
1 0
? ? x x .
07
Q.3 (a) Write an algorithm for Newton-Raphson method. 03
(b)
Find a real root of the equation 0 1 9
3
? ? ? x x in the interval [2, 3]
by the regula falsi method.
04
(c) Discuss about the pitfalls of Gauss elimination method and
techniques for improvement.
07
OR
Q.3 (a)
Prove that (i) 1 ? ? ? E , (ii)
hD
e E ?
03
(b) Fit a straight line to the following data:
x 0 1 2 3 4
y 1 1.8 3.3 4.5 6.3

04
(c) Explain the principle of least squares and using it fit an exponential
curve
bx
ae y ? to the following data :
x 0 2 4 6 8
y 150 63 28 12 5.6

07










2
u=100

Q.4 (a)
Evaluate
?
?
1
0
2
1 x
dx
using trapezoidal rule with 2 . 0 ? h .
03
(b) Using Newton?s backward difference interpolation formula find
) 40 . 0 ( f from the following table:
x 0.10 0.15 0.20 0.25 0.30
f(x) 0.1003 0.1511 0.2027 0.2553 0.3093

04
(c) Using Lagrange?s interpolation formula, find the interpolating
polynomial from the following table:
x 0 1 3 4
y -12 0 12 24

07

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
2
y x
dx
dy ?
? , where 1 ) 0 ( ? y

over [0, 3] using step size 0.5.

04
(c) Write the formula for divided differences ] , [
1 0
x x and ] , , [
2 1 0
x x x .
Using Newton?s divided difference formula find ) 9 ( f from the
following table:
x 5 7 11 13 17
f(x) 150 392 1452 2366 5202

07
Q.5 (a) Define first, second and mixed boundary value problems for elliptic
equations.
03
(b)
Find
dx
dy
at 30 . 1 ? x from the following data:
x 1.00 1.05 1.10 1.15 1.20 1.25 1.30
y 1.0000 1.0247 1.0488 1.0723 1.0954 1.1180 1.1401

04
(c) Apply fourth order Runge-Kutta method to find approximate value
of y for 2 . 0 ? x , in steps of 0.1, if
2 2
y x
dx
dy
? ? , . 1 ) 0 ( ? y
07
OR

Q.5 (a) Explain finite difference approximations to partial derivatives. 03
(b) Determine whether the following partial differential equations are
elliptic, parabolic or hyperbolic:
1.
y x
e
y
u
y x
u
x
u
?
?
?
?
?
? ?
?
?
?
?
2
2 2
2
2
2
2. ) 4 3 sin( 4 5
2
2
2
2
y x
y
u
x
u
? ?
?
?
?
?
?

04
(c) Using Gauus Seidel method up to three iterations solve the Laplace
equation 0 ? ?
yy xx
u u for the following square plate with boundary
values as shown in the figure:
u =0
02
P
12
P
22
P
01
P
11
P
21
P
10
P
20
P

07


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u =100
u =100
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