LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS
SECOND SEMESTER – APRIL 2008
MT 2500 – ALGEBRA, ANAL.GEO & CALCULUS – II
Date : 23/04/2008 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer ALL questions.: (10 x 2 = 20)
- Write the value of
- Is exact?
- State Raabe’s test.
- Define uniform convergence of a sequence.
- Find the Coefficient of in the expansion of
- Write down the last term in the expansion of
- Write the intercept and normal forms of the equation of a plane.
- Find the Centre and radius of the sphere
PART – B
Answer any FIVE questions. (5 x 8 = 40)
- Test the Convergence of
- Find the sum to infinity of the series
- Sum the series
- If a, b, c denote three Consecutive integers, show that
- The foot of the perpendicular drawn form the origin to the plane is (12,-4,-3); find the equation of the plane.
- Find the equation to the sphere through the four points (0,0,0), (a,0,0), (0,b,0), (0,0,c) and determine its radius.
PART – C
Answer any TWO questions. (2 x 20 = 40)
- a) Evaluate
- b) Find the area of the cardioid (12+8)
- a) Prove that the series
is convergent if and
- b) Sum the series
- Find the image of the point (1,3,4) in the plane . Hence prove that the image of the line is .
- Through the circle of intersection of the sphere and the plane two spheres and are drawn to touch the place . Find the equations of the spheres.