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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
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Instructions:
- Attempt any THREE questions from Q.1 to Q.6 .
- Q.7 is compulsory.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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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 € = () 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
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(b) Using bisection method, find a real root of the equation x3 — 4x — 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) Find the inverse of A= 03
(b) Find a real root of the equation 3x. 4 sinx —ex = 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
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2y +z = —8
x—2y—3z =0
—x+y+2z =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:
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| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 14 | 27 | 40 | 55 | 68 |
(c) Find the polynomial which takes the following values: 07
y(0) =1, y(1) =0, y(2) = 1and y(3) = 10. Also find y(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.
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(c) Use Lagrange’s interpolation formula to find the value of y when x = 10, if the 07 values of x and y 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 dy/dx = xy on [0,3] with 04 y(0) =1 (take h=0.25).
(c) Evaluate the integral ?01(4x — 3x2) dx by taking n=10 using 07 (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.
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| 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 ?u/?x + ?u/?y =2(x+y)u 05
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