# Loyola College Mathematics For Computer Application Question Papers Download

## 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)**

** **

- Show that is
- Prove that .
- Transform into one in which the coefficient of is unity.
- Find the first order partial derivatives for .

- Integrate with respect to
*x.*

- What is the reduction formula for .
- Solve .
- Find the general solution of Clairaut’s equation .
- How many types in Simpson’s rule?

- State the Trapezoidal Rule.

**Part B**

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

** **

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

**Part C**

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

** **

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

(b)Prove that . (8)

- (a)Solve . (12)

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

- (a)Prove that . (8)

(b)Solve the equation . (12)

- (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)