LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

SECOND SEMESTER – NOVEMBER 2012

MT 2501/2500 – ALGEBRA, ANAL.GEO & CALCULUS – II

 

 

 

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART-A

Answer ALL the questions:                                                                                                 (10 x 2=20)

1. Evaluate
2. Evaluate
3. Verify whether is exact?
4. Solve
5. Prove that the series is convergent.
6. Find the values of k for which the series
7. Prove that
8. Using binomial expansion, find the value of correct to two decimal places.
9. Find the direction cosines of the line
10. Find the centre and radius of the sphere

PART-B

 

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

11. Evaluate
12. Prove that the area and the perimeter of the cardioids are and
13. Solve
14. Solve
15. Using D’Alembert’s ratio test, examine the convergence of the series
16. Prove that
17. When is small , prove that
18. Find the equation of the plane passing through and and perpendicular to the plane

PART-C

Answer any TWO questions:                                                                                               (2 x 20=40)

 

19. a) Evaluate
20. b) Define the length of the curve and find the length of one loop of the curve
21. a) Solve when
22. b) Apply the method of variation of parameters to solve
23. a) Using Rabee’s test, Examine the convergence and divergence for the series
24. b) Prove that
25. a) Prove that the lines and are coplanar. Find the point of intersection .Also find the equation of the plane determined by the lines.
26. b) Find the equation of the sphere passing through the points,and having the centre of the sphere on the line

 

 

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