## Loyola College B.Sc. Mathematics April 2012 Algebra,Analytical Geometry And Calculus Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc., DEGREE EXAMINATION – MATHEMATICS

SECOND SEMESTER – APRIL 2012

MT 2501/MT2500- ALGEBRA,ANALYTICAL GEOMETRY AND CALCULUS

Date: 16-04-2012           Dept. No.                                                         Max. : 100 marks

Time: 9.00 – 12.00

PART-A

1. Evaluate .
2. Find x dx.
3. Define exact differential equations.
4. Solve (D22D + 1) y = 0.
5. Show that the series is convergent.
6. State Cauchy root test for convergence of a series.
7. Find the coefficient of in the expansion of 1 +  +  +  + …
8. Prove that
9. Find the direction cosines of the line joining the points (3,-5,4) and (1,-8,-2).
10. Find the angle between the planes and .

PART –B

1. Evaluate
2. Find the surface area of the solid formed by revolving the cardiodabout the initial line.
3. Solve
4. Solve .
5. Examine the convergence of
6. Assuming that the square and the higher powers of x may be neglected

show that

1. Sum to infinity the series
2. Find the shortest distance between the linesand and the equation of the line.

PART – C

ANSWER ANY TWO QUESTIONS:                                                                         (2×20= 40)

1. (a) Evaluate.

(b)  Find the length of the curve  between the points given by and.

1. (a) Solve

(b) Solve the following equation by the method of variation of parameter:

.

1. (a) Test the convergence of the series

(b)  Find the equation of the sphere passing through the points (2,3,1),(5,-1, 2),
(4,3,-1) and (2,5,3).

1. (a) Show that

(b)  Sum the series

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