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
Time : 9:00 - 12:00
Dept. No.
Max. : 100 Marks
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 z  x 2  y 2  3xy .
5. Evaluate
  2 x  1 dx .
3
6. Write down the Bernoulli’s formula for integration.
7. Find the complementary function for  D 2  4 D  3 y  cos 2 x .
8. Form partial differential equation by eliminating arbitrary constants from z  ax  by  a 2  b 2 .
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 1 3 1


11. Find the rank of the matrix  4 2 6 8  .
15 3 9 21 


sin 6
 32 cos5   32 cos3   6 cos  .
12. Prove that
sin 
13. Solve the equation x3  12 x 2  39 x  28  0 whose roots are in A.P.
 2u  2u  2u
1
2
2
2
2
14. If u  where r   x  a    y  b    z  c  ,then prove that 2  2  2  0 .
r
x y z
3
15. Evaluate  x cos x dx .
16. Solve the equation  D3  3D 2  4 D  2  y  e x .
17. Solve z  p 2  q 2 .
2
18. Apply Simpson’s 3
8
rule to evaluate
dx
 1 x
3
correct to 2 decimal places by dividing the range
0
into 8 equal parts.
Part C
Answer any TWO questions:
(2 x 20 = 40)
 2 2 3 
19. (a)Find the Eigen values and Eigen vectors of the matrix  2 1 6  .
 1 2 0 


1
(b)Prove that sin 4  cos 2   5  cos 6  2 cos 4  cos 2  2 .
2
5
4
3
20. (a)Solve 6 x  x  43x  43x 2  x  6  0 .
(b)Find the radius of curvature for the curve y 2  x3  8 at  2,0  .

21. (a)Prove that
(12)
(8)
(12)
(8)
 sin x  2

0 sin x 3 2  cos x 3 2 dx  4 .

 

3
2
(8)
(b)Solve the equation  D 2  5D  4  y  x 2  7 x  9 .
(12)
22. (a)Using Newton-Raphson method find the root of the equation x log10 x  1.2
(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
Estimate the time taken to travel 60 ft using Trapezoidal rule.
61
52
38
(5)
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