## Loyola College B.C.A. Computer Application Nov 2012 Mathematics For Computer Application Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.C.A. DEGREE EXAMINATION – COMPUTER APPLICATION

SECOND SEMESTER – NOVEMBER 2012

# MT 2101 / CS 2100 – MATHEMATICS FOR COMPUTER APPLICATION

Date : 03/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

Part A

Answer ALL questions:                                                                                                       (10 x 2 = 20)

1. Show that is
2. Prove that .
3. Transform into one in which the coefficient of is unity.
4. Find the first order partial derivatives for .
1. Integrate   with respect to x.
1. What is the reduction formula for .
2. Solve .
3. Find the general solution of Clairaut’s equation .
4. How many types in Simpson’s rule?
1. State the Trapezoidal Rule.

Part B

Answer any FIVE questions:                                                                                               (5 x 8 = 40)

1. Test for consistency and hence solve .
2. Prove that .
3. Solve the equation whose roots are in G.P.
4. Verify Euler’s theorem for the function .
5. Evaluate the double integral  if the region R is bounded by the straight lines .
6. Solve the equation .
7. Solve .
8. Evaluate   by using (i) Simpson’s  rule (ii) Simpson’s  rule.

Part C

Answer any TWO questions:                                                                                               (2 x 20 = 40)

1. (a)Find the Eigen values and Eigen vectors of the matrix .          (12)

(b)Prove that .        (8)

1. (a)Solve .                                                                     (12)

(b)Find the radius of curvature of the curve  at the points .        (8)

1. (a)Prove that .                                                               (8)

(b)Solve the equation .                                                 (12)

1. (a)Find the real root of  by false position method correct to 3 decimal places.                                                                                                                                  (15)

(b)The velocity of a particle at distance S from a point on it’s path is given by the following table

 S(ft) 0 10 20 30 40 50 60 V(ft/s) 47 58 64 65 61 52 38

Estimate the time taken to travel 60 ft using Trapezoidal rule.                                  (5)

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