LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AB 01

   B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIRST SEMESTER – November 2008

MT 1500 – ALG.,ANAL.GEOMET. CAL. & TRIGN. – I

 

 

 

Date : 10-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

 

Answer all questions:                                                                        (10 x 2 = 20 marks)

 

1. If find .
2. In the curve , prove that the subtangent is of constant length.
3. Write the formula for radius of curvature in parametric form.
4. Define evolute.
5. If is a root of find the other root.
6. Define a reciprocal equation.
7. Prove that .
8. Find .
9. Find the equation of the chord of the parabola having the mid point at .
10. Define a rectangular hyperbola.

 

PART – B

 

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

 

11. Show that in the curve the subnormal varies as the cube of the ordinate.
12. Show that the radius of curvature at any point of the catenary .
13. If where  find the minimum value of u.
14. Find the radius of curvature of the cardivid
15. Solve the equation given that  is a root of it.
16. Solve the reciprocal equation
17. Express interms of .
18. Derive the polar equation of a conic.

 

PART – C

 

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

 

19. a) If show that (1-
20. b) Find the evolute of the parabola
21. a) Solve given that it has two pairs of equal roots.
22. b) Find the positive root of the equation correct to two places of decimals, using Horner’s method.
23. a) Prove that 64
24. b) Prove that
25. a) Sum the series .
26. b) Show that in a conic the semilatus rectum is the harmonic mean between the segments of a focal chord.

 

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