Loyola College B.Sc. Physics April 2012 Mathematics For Physics Question Paper PDF Download

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 nth derivative of e4x.
  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.
  1. Find .
  2. Prove that .
  3. Write down the expansion of and  in a series of ascending powers of .
  4. Two dice are thrown. What is the probability that the sum of the numbers is greater than 8?
  5. Write a short note on binomial distribution.

 

Section B

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

  1. Find the nth differential coefficient of sinx sin2x sin3x.

 

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

 

  1. Show that .
  2. Show that the matrix is orthogonal.

 

  1. Find the Laplace transform of

 

  1. Separate into real and imaginary parts of .
  2. Prove that .

 

  1. 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)

 

  1. a) If y = acos(logx) + bsin(logx), prove that x2yn + 2 + (2n + 1)xyn + 1 + (n2 + 1)yn = 0.
  2. 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)

  1. a) Ifprove that .
  2. b) Express in a series of sines of multiples of θ.
  3. 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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