LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

XZ 3

THIRD SEMESTER – APRIL 2008

MT 3102 / 3100 – MATHEMATICS FOR PHYSICS

 

 

Date : 07/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

SECTION A

Answer ALL questions.                                                                                             (10 x 2 = 20)

 

1. Write the Leibnitz’s formula for the nth derivative of a product uv.
2. Prove that the subtangent to the curve y=a^x is of constant length.
3. Prove that =
4. Find L[e^-2tsin2t]
5. If y = log ( 1+x ).then find D²y
6. Expand tan 7q in terms of tanq
7. Prove that the matrix is orthogonal
8. If tan = tan h then show that cosx coshx = 1
9. Find the A.M. of the following frequency distribution.

x :   1    2     3      4       5       6       7

f  :  5     9    12     17    14     10      6

10. Write the general formula in Poisson’s distribution.

 

SECTION B

Answer any FIVE questions.                                                                         (5 x 8 = 40)

 

11.If y=sin^-1x, prove that  ( 1-x² )y₂ –xy₁ =o and (1-x²)y_n+2-(2n+1)xy_n+1-n²y_n=o

12.Find the length of the subtangent, subnormal, tangent and normal at the point (a,a) on the

cissoid  y² =

13. Sum to infinity the series:-

 

14. Verify Cayley Hamilton theorem for the matrix

A =

15. If sin () = tan ( x + iy) , Show that
16. If sin (A + iB) = x + iy ,

Prove that  (i)    (ii)

 

17. Find L^-1
18. Ten coins are tossed simultaneously. Find the probability of getting at least seven heads.

 

SECTION C

Answer Any TWO Questions.                                                                                   (2 x 20 = 40)

19. (a) Prove that 1 +

(b) Find the mean and standard deviation for the following table, giving the age

distribution of 542 members.

Age in years	20-30	30-40	40-50	50-60	60-70	70-80	80-90
No. of members	3	61	132	153	140	51	2

 

20.(a) Prove that  64cos⁶q – 80 cos⁴q + 24 cos²q – 1

(b) Expand sin³q cos⁴q in terms of sines of multiples of angles.                            (10 + 10)

21.a)Find the maxima and minima of x⁵-5x⁴+5x³+10

b)Find the length of the subtangent  and subnormal  at the point `t’ of the curve

x = a(cost + t sint),

y =  a(sint-tcost)                                                                                                 (10 + 10)

22. a)Solve the equation , given that y =when t = 0.

       

            b)Find L^-1                                                                                  (15 + 5)

 

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