# Loyola College B.Sc. Mathematics April 2011 Algebra, Calculus And Vector Analysis Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

THIRD SEMESTER – APRIL 2011

# MT 3501/ MT 3500 – ALGEBRA, CALCULUS AND VECTOR ANALYSIS

Date : 12-04-2011              Dept. No.                                                    Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

Answer ALL questions.                                                                                                 (10 ´ 2 = 20)

1. Evaluate
2. Find when u = x2 – y2; v = x2 + y2
3. Solve
4. Find the complete integral of z = px + qy +p2q2
5. Find grad f if f = xyz at (1, 1, 1)
6. Evaluate divergence of the vector point function
7. Find L[sin2 2t]
8. Find
9. Find the sum of all divisors of 360.
10. Find the remainder when 21000 divisible by 17.

PART – B

Answer any FIVE questions.                                                                                        (8 ´ 5 = 40)

1. Change the order of integration and evaluate
2. Express in terms of Gamma functions and evaluate
3. Solve p2 + pq = z2
4. Solve xp + yq = x
5. Show that the vectoris irrotational.
6. Evaluate: (a) L[cos 4t sin 2t]                   (b) L[e-3t sin2t]
7. Find
8. Show that 18! + 1 is divisible by 437.

PART – C

Answer any TWO questions.                                                                                       (2 ´ 20 = 40)

1. (a) Evaluate where the region V is bounded by x + y+ z = a (a > 0),
x = 0; y = 0; z = 0
.

(b)  Evaluate  where R is the region in the positive quadrant for which
x + y £ 1.

(c)  Show that

1. (a) Solve (x2 + y2 + yz)p + (x2 + y2 – xz)q = z(x+y)

(b)  Find the complete integral and singular integral of p3 + q3 = 8z

1. (a) Solve y¢¢ + 2y¢ – 3y = sin t given that y(0) = y¢(0) = 0

(b)  State and prove the Weirstrass inequality.

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

(b)  Verify Green’s theorem in the XY plane for where C is the closed curve in the region bounded by y = x; y = x2.

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