Loyola College B.Sc. Mathematics Nov 2012 Algebra, Analy. Geo., Calculus & Trigonometry Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc., DEGREE EXAMINATION – MATHEMATICS

THIRD SEMESTER – NOVEMBER 2012

MT 3501/3500 – ALGEBRA, CALCULUS AND VECTOR ANALYSIS

 

 

 

Date : 02-11-2012              Dept. No.                                        Max. : 100 Marks

Time : 9.00 – 12.00

 

PART – A

 

ANSWER ALL THE QUESTIONS:                                                                                                (10 x 2 =  20)

 

  1. Evaluate .
  2. Evaluate .
  3. Eliminate the arbitrary constants from .
  4. Find the complete solution for
  5. Find , if .
  6. Prove that div , where is the position vector.
  7. Find L(Sin2t).
  8. Find .
  9. Find the number and sum of all the divisors of 360.
  10. State Fermat’s theorem.

 

PART – B

ANSWER ANY FIVE QUESTIONS:                                                                                  (5 x 8 = 40)

  1. Change the order of integration and evaluate the integral  .
  2. Express  in terms of Gamma functions and evaluate the integral .
  3. Solve
  4. Solve
  5. Find .
  6. Find .
  7. Show that
  8. Show that is divisible by 22.

 

PART – C

 

ANSWER ANY TWO QUESTIONS                                                                                               (2x 20 = 40)

 

  1. (a) Evaluate taken over the positive quadrant of the circle .

(b)  Prove that

  1. (a) Solve

 

(b) Solve (y+z)p + (z+x)q = x+y.

 

21.(a)  Verify Stoke’s theorem for  taken over the upper half surface of

the  sphere  x2+y2 +z2 = 1, z 0 and the boundary curve C, the x2+y2  = 1, z=0.

 

(b)  State and prove Wilson’s Theorem.

  1. Using Laplace transform solve the equation given y(0) = 0 , y1(0)= -1.

 

 

 

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