University of Mumbai 2009-3rd Sem B.E Electrical and Electronics Engineering Numerical Techniques Old - Question Paper

Numerical Techniques Old Course Sem III June 2009

N.B. : (1)    Question No. 1 is compulsory.

(2)    Attempt any four questions out of remaining six questions.

<3)    Make suitable assumptions if required and justify the same.

(4)    Write programs in C/C₊₊.

1. (a) Define Inherent, Truncation and Round-off error and give an example for each.

(b) Prove that -*

(ii) n² = 1 +

(i)

(c)    Using Picard's method obtain a solution upto the fifth approximation    5 dy

-sx + y such that y 1 when x = 0. dx    7

(d)    Derive Newton-Raphson formula;    5

2.    (a) List the bracketing methods and open methods and find the real of the equation 10

_x3 - 9x + 1 =0 using bisection method correct to three decimal places.

(b) Solve the following equations by Gauss Seidel method.    10

20x + y - 2z = 17, 3x + 20y - z = -18, 2x - 3y + 20z = 25.

3.    (a) From the following table find the number of students who obtained marks 10 less than 45.

Marks 30-40 40-50 50-60 60-70 No. of students 31 42 51 35

(b) Using Newtons divided difference formula, find the value of f(9) from the 10 following table.

X 5 7 11 13 17 f(x) 150 392 1452 2366 5202

4. (a) Write a program for Lagranges interpolation and using this formula, find the 10 value of y when x = 140 from the following table.

X 110 130 160 190 y 10-8 8-1 5*5 4-8

(b) Fit a straight line to the following data by the method of least squares. 10

X 1 2 3 4 5 6 7 y 0*5 2*5 2-0 4-0 3-5 6-0 5*5

Con. 2638-VR-3060-09.    2

_P (L<0 ftTUd

5.. (a) The velocity of the trait) which starts from rest is given by the following table. 10

,the time being reckoned in minutes from the start and speed in km/hour.

; -

Time	3	6	9	12	15	18
Velocity	22	29	31	20	4	0

Estimate approximately the distance covered in 18 minutes by Simpson's 3/8^th rule.

dy

(b) Solve = x + y with x₀ = 0, y₀ = 1 by Euler's modified formula find the 10 value of y when x = 0-1 taking h = 0*05.

dy 2 2

6. (a) Solve ^{= x +} y initial conditions y{1) = 2 and find y at x = 1*2, 10

x = 1*4 by Runge-Kutta Method of Fourth Order taking h = 0-2.

(b) Using the following data, find x for which y is minimum and find this value of y. 10

X	060	0-65	0*70	0-75
y	0-6221	0-6155	0-6138	0-6170

7. (a) The current i in the electric circuit is given by i = 10e^_! sin 2jrt where t is in 10 seconds. Using Newton's method, find the value of t correct to 3 decimal places for i = 2 amp.

(b)    Write a program Simpsons 1/3^rd rule.    5

(c)    Write a short note on Golden section search.    5

Attachment: university-of-mumbai-2009-b-e-electrical-and-electronics-engineering-51118-1.pdf

Earning:   Approval pending.