b)
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1110 170 13/1800 1181510117 ೦" (1) 107911!

2y

Solve £2 - 4% + Sy = 4 e?* given that y = 2, =7 when t=0
4 dt at

८2 `

Using convolution theorem find L~*

PART C (MODULES V AND VI)
Answer two full questions.

Using Newton Raphson method find correct to four decimal places, the root

between 0 and 1 the equation x*- 6x + 4 =0

D1001

5
(s? +a?)

The population of a town is as follows

Year 1941 1951

Population 20 24
(in lakhs)

Estimate the population increase during the period 1946 to 1976

Apply Lagrange’s formula to obtain the value of y when x=35 given that

೫ 30 34 38 42
೫... 30 -13 3 18

Solve the equation using Gauss elimination method
2x+y+z=10,3x+2y+3z= 18, x+4y+9z=16

Solve the system of equations 4x + 2y+z=14,x+5y—z=10,x+y+8z=20

1961 1971
29 36

using Gauss-Seidal iteration method

A solid of revolution is formed by rotating about the x axis, the area between the x

axis, the line x=0 and x=1 and a curve through the points with the following

coordinates

Xx 0.0 0.25 0.50

Using Euler's method find y(0.2) and y(0.4) given < = > + ४, $(0) = 1 धात ॥ = 0.2

Use the fourth order Runge-Kutta method to find y(0.2) from 2 =y-x.,y(0) =2

taking h=0.1

0.75
Y 1.0000 .9896 .9589 .9089

Estimate the volume of the solid formed using Trapezoidal rule

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