# LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 ```LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – PHYSICS
THIRD SEMESTER – April 2009
ZA 06
MT 3102 / 3100 - MATHEMATICS FOR PHYSICS
Date &amp; Time: 17/04/2009 / 1:00 - 4:00
Dept. No.
Max. : 100 Marks
SECTION A
(10 x 2 = 20)
1. Find the n th derivative of
2. Find the polar subtangent and subnormal for the curve
.
3. Prove that
4. Find the rank of the matrix
5. Find
.
6. Find
7. Expand
.
.
8. Prove that
9. A letter of English alphabet is chosen at random. Find the probability that the letter so
chosen follows m and is a vowel.
10. With the usual notation state Poisson distribution.
SECTION B
(5 x 8 = 40)
11. Find the nth derivative of
.
12. Find the angle of intersection of the curves
1
and
.
13. Find the sum to infinity the series
14. Find the inverse Laplace transform of
15. If
16. Expand
prove that
.
sin 6
in terms of cos.
sin 
17. 25 books are placed at random in a shelf. Find the probability that a pair of books shall be
always together.
18. If two dice are thrown, what is the probability that the sum is greater than 8.
SECTION C
(2 x 20 = 40)
19. (a)If
prove that
(b) Find the maxima and minima of
.
(10+10)
20. (a) Find the characteristic roots and the associated characteristic vectors of the matrix
(b) Verify Cayley Hamilton Theorem for matrix
.
(12+8)
21 (a) Express
(b) Find
in a series of cosines of multiples of θ.
.
(c) Separate into real and imaginary parts of
.
(5+5+10)
22 (a) Solve
, given
and
.
(b) A coin is tossed six times. What is the probability of obtaining four or more heads?
(12+8)
2
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