LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034.

B.Sc. DEGREE EXAMINATION – MATHEMATICS

SECOND SEMESTER – APRIL 2003

 

MT 2500 / MAT 501  –  ALGEBRA ANALYTICAL GEOMETRY, cALCULUS – II

 

23.04.2003

9.00 – 12.00                                                                                                    Max : 100 Marks

 

                                                                PART – A                                       (10´ 2=20 marks)

      Answer ALL questions. Each question carries TWO marks.

 

1. Prove that
2. Evaluate
3. State cauchy’s root test for convergence of a given series.
4. Show that
5. If Y= show that
6. Solve
7. Solve where
8. Evaluate
9. Find the equation to the plane through the point (3,4,5) and parallel to the plane
10. Find the equation of the sphere with centre (-1, 2, -3) and radius 3 units.

 

 

 

                                                                PART – B                                         (5´ 8=40 marks)

      Answer any FIVE questions. Each question carries EIGHT marks.

 

11. If _n =   prove that   _.
12. Evaluate .
13. Sum the series .
14. Sum the series .
15. Solve .
16. Solve .
17. Test for convergence of the series .
18. Find the perpendicular distance from P (3, 9, -1) to the line .

 

                                                               PART – C                                         (2´20=40 marks)

Answer any TWO questions. Each question carries TWENTY marks.

 

19. a) Evaluate I =                                                                                           (10)
20. b) Find the reduction formulae for I_n =                                                  (10)
21. a) Solve by variation of parameter method.                                         (10)
22. b) Solve (10)
23. a) Sum the series (10)

 

1. b) Sum the series (10)
2. a) Show that the series  is convergent when k is greater than unity and

divergent when k is equal to or less than unity.                                                           (10)

1. Find the equation of the sphere which passes through the circle

and touch the plane            (10)

 

 

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