Math Sample Paper CBSE 2013

SECTION : A

1. If the equation x² + 8x + k = 0 has real and distinct roots, then the value of 'k' is

(a) K > 16            (b) k ≥ 16               (c) k ≤ 16                       (d) none of these

2. The probability of an impossible event is

(a) 0               (b) 1                  (c) 2                    (d) none of these

3. If the sector of a circle of diameter 10 cm subtends an angle  of 144⁰ at the centre then the length of the arc of the sector is

(a) 2π                     (b) 8π                        (c) 4π                           (d) none of these

4. If the volume of a cube is 216 cubic m  its edge is

(a) 4 cm                          (b) 6 cm                           (c) 9 cm                                    (d) none of these

5. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(a) π units
(b) 12 units
(c) 8 units
(d) none of these

6. A card is drawn from a well shuffled deck of 52 playing cards. The probability that it is not a face card is

(a) 14/52
(b) 16/13
(c) 12/52
(d) none of these

7. The distance between the points (2,3), (4,1) is

(a) 14√2
(b) 12√4
(c) 3√2
(d) none of these

8. Volume of two spheres are in the ratio 125 : 27, the ratio of their radii are

(a) 5: 3
(b) 3: 5
(c) 1: 11
(d) none of these

SECTION : B

9.        Find the roots of the quadratic equation x² – 3x – 10 = 0

10.     Find the value of 'k' for the equation 2x² + k x + 3 = 0, so that it has two equal roots.

11.     The angle of elevation of the top of a tower, at a distance of 150 m from its foot on a horizontal plane, is found to be 60⁰. Find the height of the tower.

12.     Find the centroid of triangle PQR, whose vertices are P (-3, 0), Q (5, -2), R (-8, 5).

OR

Find the coordinates of point which divides the line segment joining the points (-1, 7) and (4, -3) in the ratio 2: 3.

13.     A drinking glass is in the shape of a frustum of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.

14.     Prove that, the lengths drawn from an external point to a circle are equal.

SECTION : C

15.     A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. The common diameter is 4.2 cm and height of the cylinder and conical portion are 12 cm and 7 cm respectively. Find the volume of the solid toy.

OR

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area of toy.

16.     The sum of the reciprocals of Mohan’s age (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

17.     The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum.

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

19.     A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the ball taken out will be

                                  i.            Red

                                 ii.            Not White

20.     coin is tossed thrice. Find the probability of

                                  i.            Three tails

                                 ii.            At least two tails

21.     From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fix at the top of a 20 m high building are 45⁰ and 60⁰ respectively. Find the height of the tower.

OR

Two poles of equal heights are standing opposite to each other on the either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60o and 30o respectively. Find the height of the poles and the distances of the point from the poles.

22.     From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60o and the angle of depression of its foot is 45⁰. Determine the height of the tower.

23.     Three cows are tethered with 10 m long rope at the three corners of a triangular field having sides 42 m, 20 m and 34 m. Find the area of the plot which can be grazed by the cows, also, find the area of the remaining field ungrazed.

OR

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at the speed of 66 km/h.

24.     A chord of a circle of radius 12 cm subtends an angle of 120o at the centre. Find the area of the corresponding segments of the circle. (Use π = 3.14 and √3 = 1.73)

SECTION : D

25.     A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/h from its usual speed. Find its usual speed.

OR

Solve the equation for 'x' by using factorization method: 4x² – 4a²x + (a⁴ – b⁴)

26.     How many multiples of 4 lie between 10 and 250.

OR

Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.

27.     Find the sum :(-5) + (-8) + (-11) + ………… + (-230)

28.     Prove that the parallelogram circumscribing a circle is a rhombus.

29.     Ram, a juice seller has set up his juice shop. He has three types of glasses of inner diameter 5 cm to serve the customers. The height of the glasses is 10 cm. (Use π = 3.14)
He decided to serve the customer in "A" type of glasses.

                                  i.            Find the volume of glass of type A.

                                 ii.            Which glass has the minimum capacity?

                                iii.            Which mathematical concept is used in above problem?

                               iv.            By choosing the glass of type A, which value is depicted by juice seller Ram?