LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Sc. DEGREE EXAMINATION – PHYSICS
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THIRD SEMESTER – NOV 2006
MT 3100 – ALLIED MATHEMATICS FOR PHYSICS
(Also equivalent to MAT 100)
Date & Time : 28-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks
Section A
Answer ALL the questions (10 x 2 =20)
- Evaluate .
- Expand and .
- Prove that .
- Find when .
- Find
- Find
- Show that, in the curve , the polar subtangent varies as the square of the radius vector.
8) Find the coefficient of in the expansion of .
9) Find the rank of the matrix
10) Mention a relation between binomial and Poisson distribution.
Section B
Answer any FIVE questions (5 x 8 = 40)
11) Find
12) Find
13) If , prove that.
14) If , prove that .
15) Find the slope of the tangent with the initial line for the cardioid
at q = .
16) Find the inverse of the matrix using Cayley Hamilton
theorem.
17) Show that .
18) Suppose on an average one house in 1000 in Telebakkam city needs television
service during a year. If there are 2000 houses in that city, what is the
probability that exactly 5 houses will need television service during the year.
Section C
Answer any TWO questions only (2 x 20 = 40)
19) (a) Using Laplace transform solve when x (0) = 7.5,
x’(0) = -18.5.
(b) Prove that cosh5x = 16cosh5x – 20cosh3x + 5coshx. (12+8)
20) (a) Expand cos4q sin3q in terms of sines of multiples of angle.
(b) If prove that
(8+12)
21) (a) Find the eigen values and eigen vectors of the matrix
(b) Find the greatest term in the expansion of when . (15+5)
22) (a) Find the angle of intersection of the cardioid and
.
(b) Eight coins are tossed at a time, for 256 times. Number of heads observed at
each throw is recorded and results are given below.
| No of heads at a throw | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| frequency | 2 | 6 | 30 | 52 | 67 | 56 | 32 | 10 | 1 |
What are the theoretical values of mean and standard deviation? Calculate also
the mean and standard deviation of the observed frequencies. (10+10)
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