LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc.
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DEGREE EXAMINATION –PHYSICS
THIRD SEMESTER – APRIL 2007
MT 3100 – ALLIED MATHEMATICS FOR PHYSICS
Date & Time: 28/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
Section A
Answer ALL the questions (10 x 2 =20)
1) Evaluate.
2) Find .
3) Find .
4) If cos5q = Acosq + Bcos3q+ Ccos5q , prove that
sin5q = A sinq -Bsin3q + Csin5q.
5) If , prove that .
6) If y = e 2x, prove that .
7) Show that in the curve r = e q cot a , the polar subtangent is rtana.
8) Derive the expansion of .
9) Find the coefficient of in the series
10) Explain the concept of mutually exclusive events with an example.
Section B
Answer any FIVE questions (5 x 8 = 40)
11) Determine a, b, c so that .
12) Find L[t2 e -t cost].
13) Using Laplace transform solve , given.
14) Prove that .
15) If , prove that .
16) Verify Cayley Hamilton theorem for the matrix .
17) Sum the binomial series .
18) Assuming that half the population own a two wheeler in a city so that the chance
of an individual having a two wheeler is ½ and assuming that 100 investigators
can take sample of 10 individuals to see whether they own a two wheeler, how
many investigators would you expect to report that three people or less were
having two wheelers.?
Section C
Answer any TWO questions only (2 x 20 = 40)
19) Solve , given x(0) = 0: y(0)=2 using Laplace
transform.
20) (a) Find the real and imaginary parts of sin (x+iy) and tan(u + iv).
If , prove that .
(b) If , prove that . (10+10)
21) a) Find the angle at which the radius vector cuts the curve .
- b) A person is known to hit target in 3 out of 4 shots, whereas another person is
known to hit the target 2 out of 3 shots. Find the probability of the targets being
hit at all shots when they both try.
- c) A bag contains 5 white and 3 black balls. Two balls are drawn at random one
after the other without replacement. Find the probability that both balls drawn
are black. (10+5+5)
22) a) Find the eigen values and eigen vectors of the matrix
- b) Find the first term with a negative coefficient in the expansion of
(15+5)
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