LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – CHEMISTRY
THIRD SEMESTER – APRIL 2012
MT 3103 - MATHEMATICS FOR CHEMISTRY
Date : 28-04-2012
Time : 9:00 - 12:00
Dept. No.
Max. : 100 Marks
Part A. Answer all the questions. Each question carries two marks.
dy
1. Find
for x = a(  +sin  ); y = a(1-cos  ),
dx
x2
dy
y

log[tan(
e
)]
2. Find
if
dx
3. Evaluate  log xdx
4. Evaluate
x e
2 3x
(10 x 2 = 20)
dx
5. Prove that log 2e  log 4e  log8e  log16e  ....
x 2 x3
y 2 y3
  ... prove that x  y    ...
2 3
2! 3!
Sin  2165

7. If
, show that the angle  is 3o approximately

2166
8. Prove that sinh 3x = 3 sinh x + 4 sinh3 x
6. If y  x 
9. If the probability of defective bolt is 0.1; find the mean and standard deviation for the distribution
of defective bolts in a total of 500.
10. What are the significance of normal distribution.
Part B. Any 5 questions only. Each question carries 8 marks.
(5 x 8=40)
11. Find the equation of the tangent and normal for y2= 4ax at (at2,2at).
12. Prove that the tangents to the curve y = x2 -5x + 6 at the points (2,0) and (3,0) cut at right angles.
13. Solve (3D2- 4D + 5) y = 3 e2x

2
14. Prove that

0
sin x

dx 
4
sin x  cos x
15. If x is large, prove that
x 2  16  x 2  9 
7 175

nearly.
2 x 8 x3
sin 6
 32 cos5   32 cos3   6 cos 
sin 
17. Find the standard deviation for the following data:
Age (x)
20-25 25-30 30-35
No of
170
110
80
16. Prove that
35-40
45
40-45
40
45-50
35
frequencies (f)
18. Ten percent of the tools produced in a certain manufacturing process turn out to be defective. Find
the probability that in a sample of 10 tools chosen at random, exactly two will be defective by
using (a) Binomial distribution and (b) the Poisson approximation to the binomial distribution.
Part C. Any two questions only. Each question carries 20 marks.
1 11 1 1 1 1 1 1
19) a) Prove that log 12  1         2     3  ...
 2 3 4  4 5 4  6 7  4
19) b) Solve xp + yq = x
(2 x20 = 40)
2sin x  3cos x
20)a) Evaluate
 4sin x  5cos x dx
20)b) Evaluate
 3  2 cos x
dx
21) Find the Fourier series to the function f(x) =
1
(  x) in the interval (0,2  ).
2
22) a) Find the maximum or minimum values of xy + 1/x +1/y.
22) b) A family has six children. Find the probability P that there are (a) three boys and three girls and
(b) fewer boys than girls.
******
$$$$$$$