Andhra Pradesh Board Class 12 Math Sample Papers 2005

SAMPLE QUESTION PAPER
MATHEMATICS 
Time : 3 Hours                                                                         Max Marks : 75
Section – A
I. Very Short Answer Questions                                      10x2=20 Marks
Attempt all Questions. Each Question carries 2 marks.

1. If  x 2 + y 2 – 4x + 6y + c = 0 represents a circle with radius ‘6’, find the
value of ‘c’.

2. Find the equation of the directix of the parabola 2x2 + 7y = 0.   x2  y2

3. Find the length of the latus rectum of the ellipse  1 16          8

4. Find the eccentricity of the hyperbola   x2– 4y 2= 4

5. Find the distance between the two points in a plane whose polar
coordinates are (2, p/6) (3, p/4)

6. If y =  , then find y n.
2x + 5

7. Find    Ú   ÷1 + sin 2x dx e s i n-1 x

8. Find  Ú   dx ÷1 – x 24

9. Obtain Ú x ÷x 2 – 1 dx 1

10. State the Simpson’s rule for Numerical Integration of a function f(x)
over the interval [a,b] by dividing [a,b] into n  sub-intervals.

Section – B

II. Short Answer Questions                                            5 x 4 = 20 Marks
Attempt any five questions.  Each question carries 4 marks
11. If the line y = mx + c touches the ellipse               +             =1   a2 b 2 c2 = a2 m 2+ b2; (a > b)

12. Find the equations of the tangents shown drawn from (-2,1) to the
hyperbola     2x 2 – 3y 2= 6.

13. Transform the polar equation r  cos 2 q = a (a>0), origin as pole and the 2 +ve axis as initial line, into Cartesian form.     
log x

14. If y =  then show that x(-1)n–n 1 1 1 yn =  log x – 1 –  x n+1 2 3 n

15. Evaluate x 6– 1 dx 1 + x 2

16. Solve (x2+ y2) dx = 2 xy dy dy 2x + y + 3

17. Solve  dx 2y + x + 1

Section – C
II. Long Answer Questions                                          5 x 7 = 35 Marks
Attempt any five questions.  Each question carries 7 marks

18. Find the equation of the pair of tangents drawn from (3,2) to the circle x2+ y2– 6x + 4y – 2 = 0

19. Find the equation of the circle passing through the points of
intersection of the circles x2 + y2– 8x – 6y + 21 = 0,  x2+ y2– 2x – 15= 0 and the point (1,2).

20. Find the equation of the circle passing through the origin and coaxial
with the circles x 2 + y 2 – 6x + 4y – 8 = 0 and x 2 + y 2 – 2x + y + 4 = 0.

21.Find the pole of the line x + y + 2 = 0 with respect to the parabola y 2 + 4x – 2y – 3 = 0.3 sin x + cos x + 7

22.Evaluate          dx sin x + cos  x + 1 Ú Ú                       

23. Evaluate x 1 / 4   dx x 1 / 2  + 1

24. Find the area enclosed by the curves y = 3x and y = 6x – x 2