Download GTU B.Tech 2020 Winter 4th Sem 2140505 Chemical Engineering Maths Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 4th Sem 2140505 Chemical Engineering Maths Previous Question Paper

Seat No.: ________
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?IV (NEW) EXAMINATION ? WINTER 2020
Subject Code:2140505 Date:09/02/2021
Subject Name:Chemical Engineering Maths
Time:02:30 PM TO 04:30 PM Total Marks:47
Instructions:
1. Attempt any THREE questions from Q.1 to Q.6 .
2. Q.7 is compulsory.
3. Make suitable assumptions wherever necessary.
4. Figures to the right indicate full marks.


MARKS
Q.1 (a) Describe different types of errors.
03

(b) Find the absolute, relative and percentage errors if x is rounded-off to three
04
decimal digits. Given x = 0.005998.

(c) Find root of the equation cosx ? x ex = 0 correct up to three decimal places using
07
Secant Method. Use initial guesses 0 and 1 to obtain accuracy.
Q.2 (a) Write short note on iterative methods.
03

(b) Using bisection method, find a real root of the equation 3 - 4 - 9 = 0,
04
in four stages.

(c) Derive a recurrence formula for finding Square root of N, using Newton Raphson
07
method and hence compute square root of 27.




Q.3 (a)
1
1
3
03
Find the inverse of A = [ 1
3
-3]
-2 -4 -4

(b) Find a real root of the equation 3 + - = 0 by the method of false
04
position correct to four decimal places.

(c) Using Gauss Elimination method to solve the system of linear equations:
07
2 + = - 8
- 2 - 3 = 0
- + + 2 = 3




Q.4 (a) Explain Gauss-Jordan elimination method to solve system of linear equations.
03

(b) By the method of least squares, find the straight line that best fits the following
04
data:
x 1
2
3
4
5
y 14 27 40 55 68

(c) Find the polynomial which takes the following values:
07
(0) = 1, (1) = 0, (2) = 1 and (3) = 10. Also find (4).






Q.5 (a) Write an algorithm for Trapezoidal Rule.
03

(b) Following table shows speed in m/s and time in second of a car :
04
t 0 12
24
36
48
60
72
84
96
108 120
v 0 3.60 10.08 18.90 21.60 18.54 10.26 5.40 4.50 5.40 9.00
Using Simpson's 1/3 rule find the distance travelled by the car in 120 seconds.
1

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(c) Use Lagrange's interpolation formula to find the value of when = 10, if the
07
values of and are given below:
x 5
6
9
11
y 12 13 14 16



Q.6 (a) Write an algorithm for Newton's Forward interpolation method.
03

(b) Use Euler's method to solve the initial value problem
-
=
on [0,3] with
04
2
(0) = 1 (take h= 0.25).

(c) Evaluate the integral 1
(4 - 32) dx by taking n=10 using
07
0
(a) Trapezoidal rule (b) Simpson's 1/3 rule.
Q.7

The following data gives pressure and volume of super-heated steam. Find the
05
rate of change of pressure w.r.t. volume when V = 8.
V 2
4
6
8
10
P 105 42.7 25.3 16.7 13


OR
Q.7

Solve by method of separation of variable
+
= 2( + )
05


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