LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – NOVEMBER 2012

MT 3102/3100 – MATHEMATICS FOR PHYSICS

 

 

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION A

ANSWER ALL QUESTIONS.                                                                               (10 x 2 = 20)

1. Find the n^th derivative of .
2. Find the slope of the curve at .
3. Write the expansion for .
4. Find the rank of the matrix .
5. Find the Laplace transform of .
6. Find .
7. Write down the expansion of in powers of .
8. Show that .
9. Two dice are thrown. What is the probability that the sum of the numbers is greater than 8?
10. Define Normal distribution.

 

SECTION B

ANSWER ANY FIVE QUESTIONS.                                                                 (5 x 8 = 40)

11. Find the n^th differential coefficient of .
12. Find the maximum value of for positive values of x.
13. Find the characteristic roots of the matrix .
14. Find the Laplace transform of .
15. Express in a series of sines of multiple of .
16. Four cards are drawn at random from a pack of 52 cards. Find the probability that

(i) they are a king, a queen, a jack and an ace.

(ii) two are kings and two are queens.

(iii) two are black and two are red.

17. A car hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate the proportion of days on which (i) neither car is used, (ii) the proportion of days on which some demand is refused.
18. X is a normal variable with mean 30 and standard deviation 5. Find the probabilities that

(i) 26  X  40, (ii) X  45.

 

SECTION C

ANSWER ANY TWO QUESTIONS.                                                                 (2 x 20 = 40)

19. (a) If , then prove that .

(b) Find the length of subtangent and subnormal at any point t on the curve  and .                                                        (12 + 8)

20. (a) Verify Cayley-Hamilton theorem for the matrix and also find .

(b) Find the sum to infinity of the series . (12 + 8)

21. (a) Express in terms of .

(b) Find the mean and standard deviation for the following data:

x	10	20	30	40	50	60
f	15	32	51	78	97	109

(10 + 10)

22. (a) Solve the equation given that when .

(b) Ten coins are thrown simultaneously. Find the probability of getting at least seven

heads?                                                                                                                   (12 + 8)

 

 

 

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