LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIRST SEMESTER – NOVEMBER 2012

MT 1500 – ALGEBRA, ANALY. GEO., CALCULUS & TRIGONOMETRY

 

 

 

Date : 08/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

 

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

 

1. Write the n^th derivative of
2. If y = a show that
3. Define the evolute of a curve.
4. Find the p-r equation of the curve r = a sin q.
5. Determine the quadratic equation having 3 – 2 i as a root.
6. Diminish the roots of by 2.
7. Show that
8. Express in locus of logarithmic function.
9. Define a rectangular hyporbola.
10. Write down the angle between the asymptotes of the hyperbola

PART – B

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

 

11. Show that in the parabola the subtangent at any point is double the abscissa and the subnormal is a constant.
12. Find the radius of curvature at the point ‘O’ on
13. Show that if the roots of
14. Find the p-r equation of the curve with respect to the focus as the pole.
15. Separate into real and uniaguinary parts.
16. Find the sum of the series
17. Find the locus of poles of ale Laugets to with respect to
18. Derive the polar equation of a comic.

 

PART – C

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

 

19. a) If prove that
20. b) Show that r = a sec² and r = b cosec² intersect at right angles.
21. a) Find the minimum value of
22.        b) Find the radius of  curvature of .
23. a) Solve: given that the roots are in geometric progression.

 

1. b) Solve: .

 

22. a) Express cos8q in locus of power of sinq.

 

1. b) If e₁ and e₂ are the eccentricities of a hyperbola and its conjugate show that .

 

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