Loyola College B.Sc. Mathematics April 2008 Mathematics For Physics Question Paper PDF Download

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=ax 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

  1. 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)yn+2-(2n+1)xyn+1-n2yn=o

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

cissoid  y2 =

  1. Sum to infinity the series:-

 

  1. Verify Cayley Hamilton theorem for the matrix

A =

  1. If sin () = tan ( x + iy) , Show that
  2. If sin (A + iB) = x + iy ,

Prove that  (i)    (ii)

 

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

 

SECTION C

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

  1. (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)

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

       

            b)Find L-1                                                                                  (15 + 5)

 

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