LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

THIRD SEMESTER – APRIL 2012

MT 3102/3100 – MATHEMATICS FOR PHYSICS

 

 

Date : 28-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

Section A

Answer ALL questions:                                                                                 (10 ´ 2 = 20)

1. Find the n^th derivative of e^4x.
2. Show that in the curve rq = a, the polar sub tangent is constant.
3. Expand in ascending powers of x, ‘a’ being positive.
4. Define a symmetric matrix and give an example.

1. Find the Laplace transform of t² + 2t + 3.

6. Find .
7. Prove that .
8. Write down the expansion of and  in a series of ascending powers of .
9. Two dice are thrown. What is the probability that the sum of the numbers is greater than 8?
10. Write a short note on binomial distribution.

 

Section B

Answer any FIVE questions:                                                                           (5 ´ 8 = 40)

11. Find the n^th differential coefficient of sinx sin2x sin3x.

 

12. Find the angle of intersection of curves rⁿ = aⁿcosnq and rⁿ = aⁿ sinnq.

 

13. Show that .
14. Show that the matrix is orthogonal.

 

15. Find the Laplace transform of

 

16. Separate into real and imaginary parts of .
17. Prove that .

 

18. Calculate the mean and standard deviation for the following frequency distribution:

Class Interval	0 – 8	8 – 16	16 – 24	24 – 32	32 – 40	40 – 48
Frequency	8	7	16	24	15	7

 

Section C

 

Answer any TWO questions:                                                                        (2 ´ 20 = 40)

 

19. a) If y = acos(logx) + bsin(logx), prove that x²y_{n + 2} + (2n + 1)xy_{n + 1} + (n² + 1)y_n = 0.
20. b) Find the sum to infinity of the series .

(12 + 8)

20.a) Find the characteristic roots of the matrix .

1. b) Verify Cayley Hamilton Theorem for matrix and also find .                                                                                                              (6 + 14)
2. a) Find .
3. b) Solve the equation given that when t = 0.

(5 + 15)

22. a) Ifprove that .
23. b) Express in a series of sines of multiples of θ.
24. c) 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, and (ii) the proportion of days on which some demand is refused.                                                                                                                                            (8+5+7)

 

 

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