No. of Printed Pages: 7 IBICS-033I
DIPLOMA -VIEP -COMPUTER SCIENCE AND
ENGINEERING (DCSVI)
Term-End Examination

00353
December, 2016
BICS-033 NUMERICAL METHODS AND COMPUTATION
Time: 2 hours Maximum Marks: 70
Note: Attempt any Jive questions. Question no. 1 is compulsory. All questions carry equal marks.

1. Choose the correct answer from the given four alternatives: 7 x 2=14

Which Of the following methods has the highest rate of convergence?

Newton-Raphson Method

Secant Method

Regula-Falsi Method

None of the above

In Bisection Method, if the function has a root in the interval then the polarity of at point a and b i.e. and should be

same

opposite

both positive only

both negative only

Lagrange's interpolating polynomial for number of nodal points equal to one i.e. is given by

l0f0+ l1f1

l1f0+ l0f1

(l1

All of the above

The relation between finite difference operator and averaging operator is







None of the above


Integral(y dx) h/2[Y0 2 (Y1 Y2 ... Yn] The upper and lower limits are xn and x0 respectively,is the formula for numerical integration by

Trapezoidal Rule

Simpson's 1/3 rule

Simpson's 3/8 rule

None of the above

In divided difference table, if nth order divided difference is found to be constant, then the degree of interpolating polynomial is

n

n

n-1

None of the above

The point through which the lines of regression i.e.

and pass, is given by







None of the above

2. Find the root of the equation x^3 -9x 1 correct to three significant figures using Bisection method. 7

Use Newton-Raphson method to find the root of the equation x^3 -6x 4 correct to two decimal places. 7

3. Solve the following system of equations, by using Gauss Elimination method:

2x 2y 4z 18
x 3y 2z 13
3z= 14 7

Solve the following system of equations, by the Gauss-Seidel method. Calculate the errors after 5th iteration.


3y= 2
x-2z 7

4. Evaluate any two of the following: 7

d^2 eX

d sinx

d log x

Find Lagrange's interpolating polynomial, for the discrete data given below: 7

i 1 2
xi=0 0 3
fi=1 3 55

5. Develop Difference table and use Newton's formula, to find dy/dx and d^2y/dx^2 at x where y is given by the following values: 7 .

0.00 0.05 0.10 0.15 0.20

0.00000 0.10017 0.20134 0.30452 0.41075

Apply Trapezoidal rule to calculate

Integral )dx ,correct up to three significant figures.Take six intervals. the upper and lower limits are 1 and 0

6. Use Euler's method to solve the equation dy/dx 1-y,given initial condition is y=0. 7

Use Runge-Kutta method to approximate dy/dx=x+y,when h=0.1 and y=1 at x=0. 7

7. Apply the method of Least Squares to find the polynomial of second degree, that fits in to the data given below: 7

x 0 1.0 2.0
y 1.0 6.0 17.0

The following data is given for the marks in subjects A and in a certain examination:

A B
Mean Marks 36 85
Standard Deviation 11 8

Given the coefficient of correlation between A and 0.66.
Perform the following tasks

Determine the two equations of regression.

Calculate the expected marks in corresponding to 75 marks obtained in B

8. Explain any four of the following: 4x3 1/2=14

Initial Value Problem

Taylor Series Method for solving ODE (Ordinary Differential Equation)

Linear Programming and its Application

Types of Errors

Brent's Method