University of Mumbai 2008-3rd Sem B.E Electrical and Electronics Engineering Numerical Techniques - Question Paper

Numerical Techniques Sem III June 2008

N.B. (I)    Question Ho. I is compulsory.

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

(3)    Make suitable assumptions if required and Justify the same.

(4)    Write programs in C/C**.

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

(b)    Prove that

1    ¹    rT² [²+ ²] ii) l+

2    4

(c)    Using Picard's method solve

dy

* I + xy such that y = 0 when x = 0_t ux

(6} Derive Newton - Raphson formula.

X (a) List the bracketing methods and open methods and find the reaJ root of the equation X* 4.x 9 = 0 using bisection method correct to three decimal places.

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

27x + 6> z *85, 6*+ 15 +2* = 72, x + > + 54z = 110.

3. (a) From the following cable find the number of students who obtained marks less than 4S.

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

(b) Using Newton's divided difference formula, find the value of f[9) from the following table.

Jf	5	7	11	13	17
m	150	392	1452	2366	5202

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

X	5 1 6	9	11
y	12 13	14	1

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

X i 2 3 4 5 6 7 y 0.5 2.5 2.0 4.0 3.5 6.0 5.5

j, g: CAt'Cx*)

UVY1'

(a) The velocity of the train which starts from rest is given by the following table, the time

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

Estimate Approximately the distance covered in 18 minutes by Simpson's 3/8* rule.

(b) Solve 3x^J + 2y with Xq = 0₁ y$ = I by Euler's modified formula find the to dx

value of y when* = 0.1 taking h ss 0.05.

6. (a) Solve 4x² +y with initial conditions ,y(l) *2 and find y at x = \2,    10

dx

X = 1.4 by Runge - Kutta Method of Fourth Order taking h 0.2.

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

X 3 4 5 6 7 1 y 0.205 0.240 0.259 0.262 0*250 0.224

7. (a) Explain the propagation of errors.    5

(b)    Derive Newton Cotes integration formula and also write a program Simpson's I/3^rt rule. 10

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

Attachment: university-of-mumbai-2008-b-e-electrical-and-electronics-engineering-51162-1.pdf

Earning:   Approval pending.