1. Fill in the blanks by choosing the correct alternative.

Every polynomial equation of the nth degree has roots.

n

n+l

n+2

n-l

If has a root between a and then and are of signs.

opposite

same

negative

positive

The sum of deviation of the actual values of Y and the computed values of Y is

0

1

maximum

minimum

The relationship between E and L is .

E L

E

E

E=L

In the function Y the dependent variable Y is called

entry

argument

intermediate

interpolation

Iteration method is a method.

direct

indirect

self-correcting

step-by-step

The order of Newton-Raphson method is

1

2

3

4

Find the positive root of x -cos x 0 by bisection method.

Find the positive root of 2x^3 -3x 0 by Newton-Raphson method, correct to five decimal places.

Solve the following by method of Regula-Falsi:

x^3+2x^2+lOx-20

Solve the following system of equations by Gauss elimination method:

2x+y+4z 12

8x -3y 2z =20

4x 11y-z=33

Solve the following system of equations by Gauss-Jordan method:

10x+y+ z 12

2x 10y Z =10

5z 13

Solve the following system of equations by Gauss-Seidel method:





2z

Derive Newton's Forward interpolation formula.

From the data given below, find the number of students whose weight is between 60 and 70:

Weight in lbs: 0-40 40-60 60-80 80-100 100 -120
No. of Students 250 120 100 70 50

Using Lagrange's interpolation formula, find from the following table:

7 8 9 10
3 1 1 9

Applying Taylor series method, find the value of correct to four decimal places. Given y^2 and 1.

Apply modified Euler method and obtain y(0·2). Given dy/dx y 1.

Find given dy/dx y taking h 0.1 by Runge-Kutta method.

8. Explain any four of the following:

Linear Regression

Types of Error

Golden Section Search

Initial and Boundary Value Problems

Picard's Method

Brent's Method