LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS

THIRD SEMESTER – November 2008
MT 3500 – ALGEBRA, CALCULUS & VECTOR ANALYSIS
Date : 061108 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTIONA
Answer all questions: (10 x 2=20)
 Evaluate .
 If .
 Obtain the partial differential equation by eliminating
 Solve
 If j =j at (1, 2, 1).
 State Stoke’s theorem.
 Find .
 Find .
 Find the number and sum of all the divisors of 360.
 Find the number of integers less that 720 and prime to it.
SECTIONB
Answer any five questions: (5 x 8=40)
 Evaluate where R is the region bounded by the curves and .
 Express interms of Gamma function and evaluate .
 Solve .
 Solve .
 Show that .
 (a) Find .
(b) Find .
 Find .
 Show that (18) is divisible by 437.
SECTIONC
Answer any two questions: (2 x 20=40)
 (a) Change the order of integration and evaluate the integral.
(b) Evaluate taken over the volume bounded by the plane .
(c) Evaluate .
 (a) Solve
(b) Find a complete integral of .
 Verify Gauss divergence theorem for for the cylinderical region S given by .
 Solve .
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