# WBUT Question Papers Electronics Communication

# B Tech 3rd Semester 2007

## Numerical Methods And Programming

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**GROUP-A ( Multiple Choice Type Questions)**

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

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

a)4 b) 6

c) 3 d) 5.

2. 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.

3. 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) ;}

a) 25 b) 30

c)35 d) none of these.

iv) The degree of precision of Trapezoidal rule is

a)1 b) 2

c) 3 d) 4.

v) Which of the following methods is an iterative method ?

a) Gauss Elimination Method

c) Gauss-Jacobi Method

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<flE- 1 – A d)None of these.

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) 3x^{2} c) 6x^{2}

A^{2} x is b)d)6×6.

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

a) 2 b) 4

c) 3 d) 5.

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

a) null matrix c) identity matrix _

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

b)0.3 d)0.9

**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 |

7. 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 x^{3} – 3x- 5 = 0 by the method of false position.

Find A ~ ^{1} , if A =

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**GROUP -C ( Long Answer Type Questions )**

Answer any three of the following questions.

8.a) Find by the method of fixed point iteration the root of x^{2} – 6x + 2 * 0, which Ilea between 5 and 6 correct upto four significant figures.

b) Given ^ ^ ~ * with lntial 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.

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

method : – 5x , – x _{2} = 9 -xj+5x_{2}-x_{3} = 4 -x_{2} + 5x_{3} = -6 L 1 f x

b) Calculate by Simpson’s ^ rule, the value of the Integral I j _{+ x} dx-‘ correct

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

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

8x j – 3x_{2} + 2x_{3} = 20 ; 4x j + 1 lx_{2} – x_{3} = 33 : 6x _{l} + 3x_{2} + 12x_{3} = 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

11. 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.

C)

x : | 10 | 11 | 1-2 | 1-3 | 1-4 |

y(x): | 7-989 | 8-403 | 8-781 | 9-129 | 9-451 |

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

( 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 ^ = 1 + xy with y ( 0 ) = 2. Fin’^{1} l b’ nlue of y ( 0-2 ). 6 + 5 + 4

13. a) Write a program in C to sove the equation x^{3}-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.