IMPORTANT 50 QUESTIONS FOR CLASS X BOARD EXAMINATION FOR 2012

X MATHEMATICS   ( CBSE board exam March 2012)

1. If 4a2x2 + 4abx + = 0 has equal roots of x, then find the value of k.

2. Two positive numbers differ by 3 and their product is 504.  Find the numbers.

3. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm.  Find the diameter of the circle.

4. Two tangents PQ and PR are drawn from an external point P to a circle with centre O. Prove PROQ is a cycle quadrilateral.

5. Determine the ratio in which the point P(x, -2) divides the join of A(-4, 3) and B(2, -4).  Also find the value of x.

6. Area of a sector of a circle of radius 36 cm is 54p cm2.  Find the length of corresponding arc of sector.

7. Two cubes each of edge 4 cm are joined face to face.  Find the surface area of the resulting cuboid.

8. A dice is thrown once.  Find the probability of getting:  (a) a prime number (b) a number divisible by 2

Find the sum of all two digit positive numbers divisible by 3.

9. In an A.P. the first term is 24, the last term is 29 and the sum of all its term is 150.  Find its common difference.

10. For what values of k does (k-12)x 2 + 2(k-12)x + 2= 0 has equal roots ?

11. The circumference of the base of a 9 m high wooden solid cone is 44 m.  Find the volume of the cone.

12. A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones each of diameter 7cm and height 3 cm.  Find the number of cones so formed.

13. Find a point on x -axis which is equidistant from the points A(- 5, 4) and B(- 1, 6).

14. Show that the points A (3, 4), B(- 4, 3) and C(5, 0) lie on the circle having centre O(0,0)

15. In what ratio does the x-axis divide the line segment joining the points (- 4, - 6) and (- 1, 7).  Also find the coordinates of the point of division.

16. If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

17. AB and CD are two parallel tangents to a circle with centre O.  ST is a tangent segment between the parallel tangents touching the circle at Q.  Show that < SOT = 900.

18. An aeroplane flying horizontally 1 km above the ground

is observed at an elevation of 600.  After 10 seconds, its elevation is observed to be 300 Find the speed of the aeroplane in km/hr.

19. A tower is 60 m high.  From the top of it the angles of depression of the top and the bottom of a tree are found to be 300 and 600 respectively.  Find the height of the tree and its distance from the tower.

20. Two dice are thrown simultaneously. Find the probability of getting: 

(a) Same number on both dice.     (b)  Different numbers on both the dice.

21. Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that < APB =2 < OAB.

22. In an A.P. the sum of first ten terms is - 80 and the sum of next ten terms is - 280. Find the A.P.

23. The sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289.  Find the sum of first n terms.

24. Some students planned a picnic.  The budget for food was Rs. 480.  But 8 of them failed to go, the cost of food for each member increased by Rs. 10.  How many students attended the picnic?

25. A fast train takes 3 hours less than a slow train for a journey of 600 km.  If the speed of  the slow train was 10 km/hr less than that of the fast train, find the speeds of the trains.

26. A well of diameter 3 m is dug 14 m deep.  The earth taken out of it has been spread evenly all around it to a width of 4 m to form an embankment.  Find the height of the embankment

27. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 600.

28. If the radii of the ends of a bucket 45 cm high are 28 cm and 7 cm.  Find its capacity and surface area.

29. The angle of elevation of the top of a building from the foot of a tower is 300 and the angle of elevation of the top of the tower from the foot of the building is 600.  If the tower is 50 m high.  Find the height of the building.

30. Which term of the AP : 6, 13, 20, 27, ....... is 98 more than its 24th term ?

31. Sum of the areas of two squares is 468 m2.  If the difference of their perimeters is 24 m, find the sides of the two squares.

32. In Fig.1, two circles touch each other externally at C.  Prove that the common tangent at C bisects the other two common tangents

33. a circle touches the side BC of triangle ABC at P and touches AB and AC  produced at Q and R respectively.  Show that   AQ=  1/ 2 (Perimeter of D ABC)

34.  A(1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram ABCD taken  in order, find the values of x and y.

35. In what ratio does the y- axis divide the line segment joining the points? (24, 5) and  (3, 27).

36. Cards marked with numbers 3, 4, 5, ......, 50 are placed in a box and mixed thoroughly.  One card is drawn at random from the box.  Find the probability that the number on the drawn card is (i) divisible by 7.    (ii) Is a perfect square.

37. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm.  The total height of the toy is 31 cm.  Find the total surface area of the toy.

38. A horse is tied to a peg at one corner of a square shaped grass field of side 25 m by means of a 14 m long rope.  Find the area of the part of the field in which the horse can graze

39. Solve the following quadratic equation for x :  p2 x 2  +  (p2 -  q2)x2  -  q2 =0

40. The 4th term of an AP is equal to 3 times the first term and the 7th term exceeds twice the 3rd term by 1.  Find the first term and the common difference.

41. Draw a D ABC with BC= 8 cm,  Ð ABC= 450 and  Ð BAC= 1050.  Then construct a triangle whose sides are 2/ 3 times the corresponding sides of the DABC.

42. A circle is inscribed in a triangle ABC having sides AB58 cm, BC= 10 cm and CA = 12 cm as shown in Fig. 3.  Find AD, BE and CF.

43. If the radius of the base of a right circular cylinder is halved, keeping the height same,

Find   the ratio of the volume of the reduced cylinder to that of the original cylinder.

44. Find the area of the sector of a circle with radius 10 cm and of central angle 600.  Also, find the area of the   corresponding   major sector.  OR

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm.  Find the number of cones so formed. 

45. A man standing on the top of a multistory building, which is 30 m high, observes the  angle of elevation of the top of a tower as 600 and the angle of depression of the base of  the tower as 300.  Find the horizontal distance between the building and the tower. Also find the height of the tower.

46. An aeroplane, when 3000 m high, passes vertically above another plane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground  are 600 and 450 respectively.  Find the vertical distance between the two aeroplanes.

47. A box contains 20 balls bearing numbers 1, 2, 3, 4 , ........ 20.  A ball is drawn at random   from the box.  What is the probability that the number on the drawn ball is

(i) An odd number   (ii) Divisible for 2 or 3  (iii) Prime number (iv) Not divisible by 10

48. The mid points of the sides AB, BC and CA of a triangle ABC are D(2, 1), E(1, 0) and  F(21, 3) respectively.  Find the coordinates of the vertices of the triangle ABC.

49. ABCD is a rectangle formed by joining the points A(- 1, - 1), B(- 1, 4), C(5, 4) and D(5, - 1).  P, Q, R and S are the mid points of AB, BC, CD and DA respectively.  Is the  quadrilateral PQRS a square, a rectangle or a rhombus ?  Justify your answer.

50. The line segment joining the points A(2, 1) and B(5, - 8) is trisected at the points P and Q where P is nearer to A.  If point P lies on the line 2x- y+ k = 0, find the value of k.