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)