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
Time : 1:00 - 4:00
Dept. No.
Max. : 100 Marks
Part A
Answer ALL questions:
(10 x 2 = 20)
1. Show that 𝐴 = ( cos 𝜃
sin 𝜃
) is orthonogal.
− sin 𝜃 cos 𝜃
2. Prove that cos ℎ2 𝑥 − sin ℎ2 𝑥 = 1.
3. Transform 3x3  4 x 2  5 x  6  0 into one in which the coefficient of x 3 is unity.
4. Find the first order partial derivatives for z  x 2  y 2  3xy .
5. Integrate e5 x  2 with respect to x.
6. What is the reduction formula for  sin n x dx .
7. Solve p 2  3 p  2  0 .
8. Find the general solution of Clairaut’s equation y  xp  p 2 .
9. How many types in Simpson’s rule?
10. State the Trapezoidal Rule.
Part B
Answer any FIVE questions:
(5 x 8 = 40)
11. Test for consistency and hence solve x  2 y  3z  2, 2 x  3z  3, x  y  z  0 .
12. Prove that
cos 7
 64 cos 6   112 cos 4   56 cos 2   7 .
cos 
13. Solve the equation 3x3  26 x 2  52 x  24  0 whose roots are in G.P.
 x2  y 2 
14. Verify Euler’s theorem for the function u  sin 1 
.
 x y 
15. Evaluate the double integral
  4  x
2
 y 2  dx dy if the region R is bounded by the straight lines
R
x  0, x  1, y  0, and y 
3
.
2
16. Solve the equation ( D2  4D  4) y  e2 x .
17. Solve xp  yq  x .
10
18. Evaluate
dx
 1 x
0
2
by using (i) Simpson’s 1 rule (ii) Simpson’s 3 rule.
3
8
Part C
Answer any TWO questions:
(2 x 20 = 40)
 4 20 10 

19. (a)Find the Eigen values and Eigen vectors of the matrix  2 10
4 .
 6 30 13 


1
cos 9  cos 7  4 cos 5  4 cos 3  6 cos   .
28
20. (a)Solve x5  4 x 4  x3  x 2  4 x  1  0 .
(b)Prove that cos5  sin 4  
(b)Find the radius of curvature of the curve xy 2  a3  x3 at the points  a, 0  .

21. (a)Prove that
4

 log 1  tan   d  8 log 2 .
(12)
(8)
(12)
(8)
(8)
0
(b)Solve the equation  D 2  5D  4  y  x 2  7 x  9 .
(12)
22. (a)Find the real root of x 3  2 x  5  0 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)
*********