University of Mumbai 2009-3rd Sem B.Sc Information Technology (IT) Computational Mathematics - Question Paper

Kindly obtain the attachment.

ZN-1515

10

10

G'c- Cx"0

N.B. : (1) Question No. 1 is compulsory.

(2)    Attempt any four from the remaining questions.

(3)    All questions carry equal marks.

1.    (a) To find root of an equation x³ - 2x + 5 = 0 using bisection method.

(b) To find root of an equation x³ - 2x - 1 =0 using regular falsi method.

2.    (a) Solve the equation by Gauss Seidel method :

27x + 6y - z = 85 6x + 1 5y + 2z = 72 x + y + 54z =110 (b) Solve the equation by Gauss elimination method :

2x y + 2z = 2 x + 1 Oy 3z = 5 x y z = 3

3.    (a) Using Newton's Forward Interpolation method :

X 20 23 26 29 y 0-3420 0-3907 0-4384 0-4848

6

(b) Evaluate (* ^d- by using trapezoidel rule. Devide the interval (0, 6) into 6 parts 10

J 1 + X² o

each of with h = 1.

4. (a) Use Lagrange's Interpolation formula to find the value of 'y' when x = 10

10

I X	5	6	9	, 11
y	12	13	14	16

u

(b) Evaluate J ^dx ₃- by using Simpson's 3/8 rule and Simpsons 1/3 rule. Devide interval 10

(0, 6) into 6 parts each of with h = 1.

with initial value of y (0) = 1, h = 0-2. Using Euler's modified method 10

and find y (0-6) = ?

(b) Solve y' = x + y. To find y when x = 0-5, y (0) = 1 using Eulers method.

X	0	5	10	15	20	25
y	12	15	17	22	24	30

(b) To solve the following L.P.P. equation to maximize z = 5x + 10y. Subject to the 10 constraints,

5x + 8y < 40

3x + y < 12

x, y >0.

By graphical method.

Attachment: university-of-mumbai-2009-b-sc-information-technology-51559-1.pdf

Earning:   Approval pending.