# Loyola College B.Sc. Physics Nov 2006 Allied Mathematics For Physics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034  B.Sc. DEGREE EXAMINATION – PHYSICS

 AA 03

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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