LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

XZ 54

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)

1. Evaluate
2. Write the value of
3. Is exact?
4. Solve
5. State Raabe’s test.
6. Define uniform convergence of a sequence.
7. Find the Coefficient of in the expansion of
8. Write down the last term in the expansion of
9. Write the intercept and normal forms of the equation of a plane.
10. Find the Centre and radius of the sphere

 

 

PART – B

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

 

1. Evaluate
2. Solve
3. Test the Convergence of
4. Find the sum to infinity of the series
5. Sum the series
6. If a, b, c denote three Consecutive integers, show that

1. The foot of the perpendicular drawn form the origin to the plane is (12,-4,-3); find the equation of the plane.
2. 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)

1. a) Evaluate

1. b) Find the area of the cardioid (12+8)

1. a) Prove that the series

is convergent if and

1. b) Sum the series

1. Find the image of the point (1,3,4) in the plane . Hence prove that the image of the line is .
2. 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.

 

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