LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – MATHEMATICS

AB 07

THIRD SEMESTER – November 2008

MT 3500 – ALGEBRA, CALCULUS & VECTOR ANALYSIS

 

 

 

Date : 06-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION-A

Answer all questions:                                                                        (10 x 2=20)

 

1. Evaluate .
2. If .
3. Obtain the partial differential equation by eliminating
4. Solve
5. If j =j  at  (1, -2, -1).
6. State Stoke’s theorem.
7. Find .
8. Find .
9. Find the number and sum of all the divisors of 360.
10. Find the number of integers less that 720 and prime to it.

 

 

SECTION-B

Answer any five questions:                                                              (5 x 8=40)

 

1. Evaluate  where R is the region bounded by the curves and .
2. Express interms of Gamma function and evaluate .
3. Solve .
4. Solve .
5. Show that .
6. (a) Find .

(b) Find .

1. Find .
2. Show that (18) is divisible by 437.

 

 

SECTION-C

Answer any two questions:                                                                          (2 x 20=40)    

 

1. (a) Change the order of integration  and evaluate the integral.

(b) Evaluate  taken over the volume bounded by the plane .

(c) Evaluate .

1. (a) Solve

(b) Find a complete integral of .

1. Verify Gauss divergence theorem for  for the cylinderical region S given by .
2. Solve .

 

 

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