Madras University (UnOM) 2006 M.C.A Computer Mathematical Foundation for Science - Question Paper

Time: 3 hours
Maximum: 75 marks

PART A - [5 x five = Marks 25]

ans ALL ques..

All ques. carry equal marks.

1. (a) Show that ~ (P v Q) is equivalent to P A Q.
Or
(b) A learner is to ans 10 out of 13 ques. in an exam.
(i.)How many options has he?
(ii) How many options he has, if he must ans the 1st 2 questions?

2. (a) obtain the g.c.d. (8316, 10920).
Or
(b) obtain the units in (Z10 + 10

3. (a) discuss the iterative method to obtain a root off W= 0.
Or
(b) obtain a root of x three - 2x - three = 0 using Newton Raphson method.

4. (a) discuss Gauss-elimination method to solve Ax =b.
Or
(b) How Cholesky decomposition is useful in solving the system of equations?

5. (a) obtain f'(0-2) from the subsequent
X 0.2 0.4 0.6 0.8 1.0
f(x) 1.16 3.56 13.96 41.96 101.00
Or
(b) discuss Simpson's three rule for numerical eight integration.

PART B - [5 x 10 = Marks 50]

ans any 5 ques..

All ques. carry equal marks.

6. Prove that R A (P V Q) is a valid conclusion from

the premises P v Q, Q --> R, P -> M and ~ M.

7. Construct the multiplication table for symmetric

group S3 -

8. Show that in any ring R,

(a) a.0=0

(b) a - (-b) = -ab

(c) (-a) (-b) = ab for all a, b e R.


9. obtain the 1st approximation of the root of the formula x three - 3x - five = 0 using Muller's method which lies ranging from two and 3.

10. Using Gauss-Jacobi solve the subsequent system

83x + 11y - 4z = 95

7x + 52y + 13z = 104

3x + 8y + 29z = 71.


1 one by Gauss3

3 five one 1

11. obtain the inverse of A= four three -1



Jordan method.

12. Using the Richardson's extrapolation limit, obtain Y'(0.05) to the function y one with

X

h = 0.0128, 0.0064, 0.0032.



F2 -x two 12dX

13. calculate the integral I= e using

0

Trapezoidal rule by taking 0.125.

Earning:   Approval pending.