b)
a)

b)

a)

b)

a)

b)

0)

ಖ

0)

0)

Find the Laplace transform of (i) 107911!

2y

Solve 22 - 4% + Sy 4 ९३८ given that y = 2, =7 when {= 0
4 at at

ಣಿ.

Using convolution theorem find 1 1

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

D1001

5
(52 +a?)

(1)

Pages: 2

(8)

(7)

(8)

Using Newton Raphson method find correct to four decimal places, the root (8)

between 0 and 1 of the equation x*- 6x + 4 ಎ0

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

Solve the equation using Gauss elimination method

2x+y+z=10,3x+2y+3z=18, x+4y+9z=16

1961 1
29 36

(12)

(6)

(7)

Solve the system of equations 4x + 2y+z=14,x+5y—z=10,x+y+8z=20 (7)

using Gauss-Seidal iteration method

A solid of revolution is formed by rotating about the x axis, the area between the ೫ (7)

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

coordinates

Xx 0.0 0.25 0.50

0.75
Y 1.0000 .9896 .9589 .9089

Estimate the volume of the solid formed using Trapezoidal rule

1.00
8415

Using Euler's method find y(0.2) and y(0.4) given < = > + 9, y(O) = 1 10 ॥ = 0.2 (6)

Use the fourth order Runge-Kutta method to find y(0.2) from 2 =y-x.,y(0) ಎ2 (7)

taking h=0.1

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