LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

           B.Sc. DEGREE EXAMINATION – MATHEMATICS

XZ 8

THIRD SEMESTER – APRIL 2008

MT 3501 – ALGEBRA, CALCULUS AND VECTOR ANALYSIS

 

 

 

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

Time : 1:00 – 4:00

SECTION – A

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

1. Evaluate .
2. If find the Jacobian of x and y with respect to r and .
3. Solve
4. Find the complete solution of

.

1. Find  at (2,0,1) for .
2. State Stoke’s theorem.
3. Evaluate ë (Sinh at).
4. Evaluate ë^-1.
5. Find the sum of all divisors of 360.
6. Compute (720).

 

SECTION – B

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

1. By the changing the order of integration evaluate

 

1. Express  interms of Gamma function and evaluate .
2. Obtain the complete and singular solutions of .
3. Solve.
4. Find  if
5. Evaluate (i) ë   (ii) ë
6. Find  ë^-1
7. Show that if x and y are both prime to the prime n, then x^n-1-y^n-1 is divisible by n. Deduce that x¹²-y¹² is divisible by 1365.

 

 

 

SECTION – C

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

1. a) Evaluate over the tetrahedron bounded by the planes  and the coordinate planes.

1. b) Show that .
2. c) Using gamma function evaluate.

1. a) Solve

1. b) Solve the following by Charpit’s method

 

1. c) Solve

1. a) Verify Green’s theorem for  where C is the region bounded by y=x and y=x^2.

437. b) Show that 18!+1 is divisible by 437.

1. a) State and prove Wilson’s theorem.

1. b) Solve given using Laplace

 

Go To Main page

 

Latest Govt Job & Exam Updates:

View Full List ...