1. Choose the correct answer from the given four alternatives:

(a) The forward difference operator is denoted by the symbol delta

(ii) omega

(iii) nabla

(iv) infinity In the function y the dependent variable is Y

(ii) x

(iii) a constant The polynomial equation of the nth degree has roots. n

(ii) n 1

(iii) n 2
n-1 The order of Newton-Raphson method is 1

(ii) 2

(iii) 3

(iv) 4 The error in the trapezoidal rule is of the order h

(ii) h^2

(iii) h^3
4 Fourth degree equations are also called equations. quadratic

(ii) cubic

(iii) linear
bi-quadratic In the function y the independent variable is y
x

(iii) a constant

2.(a) Find the positive root of x^3 1 and correct to four decimal places by bisection method.

(b) Using Newton's method, find the root between 0 and 1 of x3 6x and correct to five decimal places.

3.(a) Solve for a positive root of x3-4x 1=0 by Regula-Falsi method.

(b) Solve the system of equations by Gauss elimination method.

x 2y z=3

2x 3y 3z 10

3x-y 2z 13

4.(a) Solve the system of equations by Gauss-Jordan method.

2x y 4z= 12

8x-3y 2z=20

4x 11y-z 33
Solve the system of equations by Gauss-Seidel method.

8x-6y z 13.67

3x y-2z 17.59

2x-6y 9z =29.29

5.(a) What are the merits and demerits of Lagrange's formula ?Discuss. The following data are taken from the steam table:

Temp 140 150 160 170 180
Pressure: 3·685 4·854 6·302 8·076 10·225

Find the pressure at temperature t 142°.

6.(a) Using Lagrange's interpolation formula, find the value of y at x 5 from the following table:

x: 1 2 3 4 7
y: 2 4 8 16 128
Applying Taylor series method, find, correct to four decimal places, the values of y(1·1) and given dy/dx and =1.

7.(a) Using Euler's method, find given xy, 1. Evaluate given dy/dx y(1·2) by Runge-Kutta method.

8. Explain any four of the following:

(a) Linear Programming Cramer's Rule Types of Errors Golden Section Search Picard's Method Triangularization Method