# WBUT Exam Papers EC

## Numerical Methods And Programming B Tech Sem Third Dec 2007

Time : 3 Hours ]

[ Full Marks : 70

GROUP-A ( Multiple Choice Type Questions)

1. Choose the correct alternatives for any ten of the following :   10 x 1 = 10

1) The no. of significant digits in 1*00234 is

a)      4                   b) 6

c) 3                      d) 5.                     1

• IQ Which of the following relations is / are true ?

a)        A . V = A – V b) A . V = A + V

c) A . V = A / V          d) all of these.         |

1U) The output of the following program will be :

#include<stdio.h> main()

{

int i = 0, x = 0 ; while (i < 0) { if (i%5 = = 0 ) { x + = i;}

++ i; } printft “\nx = %d”, x) ;

}

25                    b) 30

35                    d) none of these.

iv)            The degree of precision of Trapezoidal rule is

Gauss Elimination Method

c)  Gauss-Jacobi Method

’ h ■ ■ .

vi)             Method of Bisection is

a)  conditionally convergent

c)               non-conveigent

b)               Gauss-Jordan Method

d)               Crout’s Method.

b)                always Convergent

d)                none of these.

vii)     Which of the following relations is true ?

a)        E – 1 + A b)

c)         E = 1/ A     <fl

viii)         Regula-Falsi Method is used to

a)   find the root of a system of linear simultaneous equations

b)              differentiate

c)               find the root of an algebraic or transcendental equation

d)              solve linear differential equations.

 ix} The value of a) 3x2 c) 6x2
 6x 6.
 b) d)

x) The order of h in the error expression of Simpson’s l/3rd rule is

a)                                                                                                                           2   b) 4

c)                                                                                                                            3   d) 5.

. ttXL AIJ-t , i

xl) When Gauss Elimination method is used to solve AX = B, A is transformed to a

b)                  upper triangular matrix

d)                 diagonally dominant matrix.

Mi) If = x + y and y ( 1 ) = 0, then y ( 1.1) according to Euler’s method is ( h = 0.1 J.

 a) 0.1 c) 0.5
 0.3 0.9.
 b) d)

GROUP -B ( Short Answer Type Questions )

Answer any three of the following.

Given the following table, find f{x) and hence find /( 6 )

 x : 0 1 2 3 4 5 f(x): 41 43 47 53 61 71

3. The values of sin x are given below, for different values of x. Form a difference table and from this table find the sin 32°.

 x : 30° 35° O o 45° 50° 55° y m sin x : 0-5000 0-5736 0-6428 0-7071 0-7660 0-8192

What are subscripts ? How are they written ? What restrictions apply to the values that can be assigned to subscripts ?

Evaluate V12 to three places of decimals by Newton-Raphson method.

Find a root of the equation x3 – 3x- 5 = 0 by the method of false position.

8-4

Find A ~ 1 , if A =

-4 8-4 V 0 -4 8 ) by Gauss-Jordan method.

GROUP -C ( Long Answer Type Questions )

Answer any three of the following questions.                         3 x 15 » 45

1. a) Find by the method of fixed point iteration the root of x2 – 6x + 2 * 0, which Ilea

between 5 and 6 correct upto four significant figures.

b)               Given ^ ^ ~ * with lntlal condition y = 1 at x = 0, find y for x = 0-1 by ax y t x

Euler’s method, correct upto 4 decimal places, taking step length h = 0-02.

10 + 5

1. a) Solve the following system of linear equations by Gauss-Jordan elimination

method : –

5x , – x 2 = 9 -xj+5x2-x3 = 4 -x2 + 5x3 = -6

l

1                                                           f x

b  Calculate by Simpson’s ^ rule, the value of the Integral I j + x dx.’ correct

o

upto three significant figures by taking six intervals.                                              10 + 5

1. a) Solve the following system of equations by LU-factorization method :

8x j – 3x2 + 2x3 = 20 ; 4x j + 1 lx2 – x3 = 33 : 6x l + 3x2 + 12x3 = 36.

b)               Using Gauss-Seidel method, find the solution of the foUowlng system of the linear equations correct upto 2 place of decimal.

3x+y + 5z =13, 5x- 2y + z = 4, x + 6y – 2z = – 1.                                       8 + 7

1. a) Find /( 0-9 ) by using Newton divided difference formula. Given
 x ; 0 1 2 4 fix): 5 14 41 98

b) Estimate the missing values from the following table :

 x ; 1 3 5 7 9 11 V : 2 ? 27 64 ? 216

State the necessary assumption.

 x : 10 11 1-2 1-3 1-4 y(x): 7-989 8-403 8-781 9-129 9-451

5 + 5 + 5

1. a) Solve the equation ^ = x2 + y 2 : y ( 0 ) = 1. for x = 01 by using Runge-
2. Kutta 4th order method and find the solution correct upto 4 place of diclmal.

( h = 0 05 )

b)               Find the solution of the following differential equation by Euler s method for x = 1. by taking h = 0-2, ^ = xy, with y = 1 when x = 0.

c)               Using Taylor’s series method solve ^ – I + xy with y ( 0 ) = 2. Fin’1 l b’ nlue of y ( 0-2 ).       6 + 5 + 4

1. a) Write a program in C to sove the equation x3-x-4 = 0 within ( 1. 2 ) by

Bisection method, correct upto 3 place of decimals.

b)               Solve the equation jjj* = x + y with intial condition y ( 0 ) = 10 and h = 0-1. using predictor-corrector method, to find y ( 0-2 ).

c)               Write a program in C using recursive function to calculate the sum of all digits of any number.                                                                                                                             6 + 5 + 4

END