Madras University (UnOM) 2006 M.C.A Computer Mathematical Foundation for Science - Question Paper
Tuesday, 13 August 2013 02:25Web
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. |