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

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.C.A. DEGREE EXAMINATION – COMPUTER APPL.

SECOND SEMESTER – APRIL 2012

# MT 2101 – MATHEMATICS FOR COMPUTER APPLICATIONS

Date : 23-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

Part A

Answer ALL questions:                                                                               (10 x 2 = 20)

1. Give an example of skew symmetric matrix.
2. Prove that .
3. If α and β are the roots of the equation, find α+β, αβ.
4. Find the first order partial derivatives for .
5. Evaluate .
6. Write down the Bernoulli’s formula for integration.
7. Find the complementary function for .
8. Form partial differential equation by eliminating arbitrary constants from .
9. Write the approximation formula to find the root using Regula Falsi method.
10. How many types in Simpson’s rule.

Part B

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

1. Find the rank of the matrix .
2. Prove that .
3. Solve the equation  whose roots are in A.P.
4. If  where ,then prove that .
5. Evaluate .
6. Solve the equation .
7. Solve .
8. Apply Simpson’s  rule to evaluate  correct to 2 decimal places by dividing the range into 8 equal parts.

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 for the curve  at .                                    (8)

1. (a)Prove that .                                                             (8)

(b)Solve the equation .                                                 (12)

1. (a)Using Newton-Raphson method find the root of the equation       (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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