Loyola College B.Sc. Mathematics April 2008 Algebra, Calculus & Vector Analysis Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

           B.Sc. DEGREE EXAMINATION – MATHEMATICS

XZ 7

THIRD SEMESTER – APRIL 2008

MT 3500 – ALGEBRA, CALCULUS & VECTOR ANALYSIS

 

 

 

Date : 26-04-08                  Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL questions:                                                                    (10 x 2 = 20 marks)

  1. Show that G (n+1) = n G(n).
  2. Show that
  3. Form the partial differential equation by eliminating the arbitrary function from .
  4. Solve:
  5. Show that is solenoidal.
  6. Show that curl
  7. Find  ë .
  8. Find ë .
  9. Define Euler’s function.
  10. Find the number of integer, less than 600 and prime to it.

 

PART – B

Answer any FIVE  questions:                                                          (5 x 8 = 40 marks)

  1. Show that.
  2. Show that é
  3. Solve:
  4. Find the general integral of
  5. Find the directional derivative of xyz-xy2z3 at(1,2,-1) in the direction

of

  1. If find where C is the curve y=2x2 from (0,0) to (1,2).
  2. Find ë  if

for

  1. With how many zeros does         end.

                                                            

PART – C

Answer any TWO   questions:                                                          (2 x 20 = 40 marks)

  1. a) Evaluate
  1. b) Evaluate over the region in the positive octant for which .
  1. a) Find the complete integral of using charpits method.
  1. b) If where is a constant vector and is the position vector of a point show that curl .
  1. a) Verify Stoke’s theorem for

where S is the upper half of the sphere  and C its boundary.

  1. b) Find (i) ëùand (ii) ëù
  1. a) Solve using Laplace transforms

given that

and at t = 0.

  1. b) Find the highest power of 11 in     .

 

 

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