CBSE Math Previous year Question paper

 

1. Find the value of p so that the quadratic equation Px(x – 3) + 9 = 0 has two equal roots. (2 Marks)

2. Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other (2 Marks)

3. Find the value of k for which x = 2 is a solution of the equation kx² + 2x – 3 = 0 (1 Marks)

4.  Find the value/s of k for which the quadratic equation 3x² + kx + 3 = 0 has real and equal roots. ( 1 Marks)

5. Find all the zeroes of the polynomial x⁴+ x³– 14x² – 2x + 24, if two of its zeroes are   and – . (3 Marks)

6. Solve the quadratic equation 2x² +ax – a² = 0 for x (2 Marks)

7. Find the values of k for which the quadratic equation (k + 4) x ² + (k + 1)x + 1 = 0 has equal roots. Also find these roots.  (4 Marks)

8. Find the roots of the equation 1/x+4 – 1/x-7 = 11/30 (4 Marks)

9. If 1 is a root of the equations ay2 + ay + 3 = 0 and y² + y + b = 0, then find the value of ab. (1 Marks)

10. The Diameter of base of a right circular is 28 cm and its height is 21 cm. Find its
(i) Curved Surface area  

(ii) Total Surface area 

(iii)Volume   (3 Marks)

11. The angles of a triangle are in A.P., the least being half the greatest. Find the angles. (2 Marks)

12. Find a relation between x and y such that the point P(x, y) is equidistant from the points A (2, 5) and B (-3, 7). (2 Marks) 13. The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30°. If the ships are 200 m apart, find the height of the light house. ( 2 Marks)

14. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then calculate the height of the wall. (1 Marks)

16. If p, q, r and s are in A.P. then r – q is (a) s – p        (b) s – q          (c) s – r     (d) none of these

17. The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is (a) -955 (b) -945 (c) -950  (d) -965

18. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, the length of the wire is (a) 6 m (b) 10 m (c) 12 m (d) 20 m

19. The total surface area of a hemispherical solid having radius 7 cm is (a) 462 cm² (b) 294 cm² (c) 588 cm² (d) 154 cm²

20. The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are
(a) 9 : 25       (b) 5 : 3       (c) 9 : 5       (d) 3 : 25

21. If sin A – cos A = 0, then the value of sin⁴ A + cos⁴ A is (a) 2 (b) 1 (c) 3/4 (d) ½

22. The distance between the point P(1, 4) and Q(4, 0) is (a) 4 (b) 5 (c) 6  (d) 3√3

23. If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is  (a) -7 or -1 (b) -7 or 1 (c) 7 or 1 (d) 7 or -1

24. If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is (A) 4πr² (B) 6πr² (C) 3πr² (D) 8πr²

25. The 21st term of the AP whose first two terms are –3 and 4 is (A) 17     (B) 137      (C) 143        (D) –143