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
ANSWER ALL QUESTIONS: (10×2 =20)
- Evaluate .
- Find x dx.
- Define exact differential equations.
- Solve (D22D + 1) y = 0.
- Show that the series is convergent.
- State Cauchy root test for convergence of a series.
- Find the coefficient of in the expansion of 1 + + + + …
- Prove that
- Find the direction cosines of the line joining the points (3,-5,4) and (1,-8,-2).
- Find the angle between the planes and .
ANSWER ANY FIVE QUESTIONS: (5×8=40)
- Find the surface area of the solid formed by revolving the cardiodabout the initial line.
- Solve .
- Examine the convergence of
- Assuming that the square and the higher powers of x may be neglected
- Sum to infinity the series
- Find the shortest distance between the linesand and the equation of the line.
PART – C
ANSWER ANY TWO QUESTIONS: (2×20= 40)
- (a) Evaluate.
(b) Find the length of the curve between the points given by and.
- (a) Solve
(b) Solve the following equation by the method of variation of parameter:
- (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).
- (a) Show that
(b) Sum the series