LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
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)
- Evaluate .
- If find the Jacobian of x and y with respect to r and .
- Find the complete solution of
- Find at (2,0,1) for .
- State Stoke’s theorem.
- Evaluate ë (Sinh at).
- Evaluate ë-1.
- Find the sum of all divisors of 360.
- Compute (720).
SECTION – B
Answer any FIVE questions. (5 x 8 = 40 marks)
- By the changing the order of integration evaluate
- Express interms of Gamma function and evaluate .
- Obtain the complete and singular solutions of .
- Find if
- Evaluate (i) ë (ii) ë
- Find ë-1
- Show that if x and y are both prime to the prime n, then xn-1-yn-1 is divisible by n. Deduce that x12-y12 is divisible by 1365.
SECTION – C
Answer any TWO questions. (2 x 20 = 40 marks)
- a) Evaluate over the tetrahedron bounded by the planes and the coordinate planes.
- b) Show that .
- c) Using gamma function evaluate.
- a) Solve
- b) Solve the following by Charpit’s method
- c) Solve
- a) Verify Green’s theorem for where C is the region bounded by y=x and y=x2.
- b) Show that 18!+1 is divisible by 437.
- a) State and prove Wilson’s theorem.
- b) Solve given using Laplace