Indira Gandhi National Open University (IGNOU) 2005 B.Tech Water Resource Engineering Computer Programming and Numerical Analysis - Question Paper

Test Papers / Previous ques. Papers of IGNOU ET302 (A) Computer Programming & Numerical Analysis December 2005
B.Tech. Civil (Construction Management) /
B.Tech. Civil (Water Resources Engineering)
Term-End exam

December, 2005

ET-302(A) : COMPUTER PROGRAMMING & NUMERICAL ANALYSIS

Time: three hours
Maximum Marks: 70

Note : Attempt any 5 ques.. All ques. carry equal marks. Use of calculator is allowed.
1. (a) Perform 3 iterations of the Regula - Falsi method to obtain the root of the formula x4 - x - 10 = 0 in the interval [1, 2]. presume suitable initial approximations.

(b) Consider the subsequent system of equations :
4x - y + z = 7
4x - 8y + z = - 21
-2x + y + 5z = 15
Perform only 4 iterations of Jacobi iteration or Gauss - Seidel itertion method for solving the equations. presume (xo, yo, zo) = (1,2,2) to begin with. (7,7)

2. (a) Use the LU decomposition method to solve the system of equations :
x + y + z = 1
4x + 3y - z = 6
3x + 5y + 3z = 4

(b) obtain the dominant eigenvalue and the corresponding eigenvector accurate to 2 decimal places of the matrix

two -1 0
A = -1 two -1
0 -1 2Using the power method and carry out 4 iterations. (7,7)

3. (a) Verify the equivalence of the subsequent relations :

(i) ?2 cos (2x) = -4 sin2h cos (2x + 2h)

(ii) (?2/E) x3 = 6x

(iii) E (2µd - ?) = ?

(b) Using Muller's method, obtain a root of the formula x3 - x2 - x - one = 0 which lies ranging from three and four accurate to three decimal places. (6,8)

4. (a) The values of a polynomial of degree five are tabulated beneath. If f(4) is known to be in error, obtain its accurate value. x: 2.5 3.0 3.5 4.0 4.5 5.0 5.5
f(x): 4.32 4.83 5.27 5.47 6.26 6.79 7.23


(b) In the table beneath. the values of y are consecutive terms of a series of which 43 is the sixth term. obtain the 1st and the 10th terms of the series. x: three four five six seven eight nine
y: 4.8 8.4 14.5 23.6 36.2 52.8 73.9


5. (a) Solve the subsequent system of linear equations with Gaussian elimination method :
2x1 - 2x2 + 5x3 = 6
2x1 + 3x2 + x3= 13
-x1 + 4x2 - 4x3 = 3

(b) obtain Lagrange's interpolating polynomial for the subsequent data. Also find the value of f(2) using polynomial. x 0 one four five
f(x) eight 11 68 123


6. (a) Using 2nd order Taylor series method upto the terms of h2 solve the equation, dy/dx = 3x + y/2; y(0) = 1. obtain y(0.4) taking h=0.2.

(b) Solve the differential formula
dy/dx = 1/x2 - y/x - y2, y(1) = -1 by Runge - Kutta method for x = one to x = 5/3 in steps of h = 1/3 by carrying out computation in 2 steps. (7, 7)

7. (a) The sum of the squares of the 1st n natural numbers is provided by


n(n+1)(2n+1)
s = ----------------
6
Write a program that will obtain s for n = 10 (10) 250, i.e., n = 10, 20, 30, ....., 250

(b) Using logical IF statements, write a program that calculates and prints


f(x) = {3x + 5x3 for 4.3=x<9.1
{6x + 8x2 for 9.1=x<15.5for x varying from 5.0 to 15.0 in steps of 0.5 (7, 7)

8. (a) The values of x are to be tabulated from the formula
x = (sin t e-2t + log t) / (5t - cos t)
for t = 1.0 to 5.0 in steps of 0.1 Write a program to calculate and print x for every value of t in the provided range.

(b) Write a program to calculate ?n. Test for n = 0, one and 3. (7,7)

Earning:   Approval pending.