LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – PHYSICS
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THIRD SEMESTER – April 2009
MT 3102 / 3100 – MATHEMATICS FOR PHYSICS
Date & Time: 17/04/2009 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL questions: (10 x 2 = 20)
- Find the n th derivative of
- Find the polar subtangent and subnormal for the curve .
- Prove that
- Find the rank of the matrix
- Find .
- Find .
- Expand .
- Prove that
- A letter of English alphabet is chosen at random. Find the probability that the letter so chosen follows m and is a vowel.
- With the usual notation state Poisson distribution.
SECTION B
Answer any FIVE questions: (5 x 8 = 40)
- Find the nth derivative of .
- Find the angle of intersection of the curves and .
- Find the sum to infinity the series
- Find the inverse Laplace transform of
- If prove that .
- Expand in terms of cosq.
- 25 books are placed at random in a shelf. Find the probability that a pair of books shall be always together.
- If two dice are thrown, what is the probability that the sum is greater than 8.
SECTION C
Answer any TWO questions: (2 x 20 = 40)
- (a)If prove that
(b) Find the maxima and minima of . (10+10)
- (a) Find the characteristic roots and the associated characteristic vectors of the matrix
(b) Verify Cayley Hamilton Theorem for matrix .
(12+8)
- (a) Express in a series of cosines of multiples of θ.
(b) Find .
(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)
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