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CBSE CLASS X

Mathematics

General Instructions:

1. All questions are compulsory. There are three sections A, B, C and D in the question paper. 


2. Section A: Q. Nos. 1 to 8 carry 1 mark each.
   Section B: Q. Nos.9 to 14 carry 2 marks each.
   Section C: Q. Nos. 15 to 24 carry 3 mark each.
   Section D: Q. Nos. 25 to 34 carry 4 mark each.


3. There is no overall choice, however internal choices has been provided in one question of 2 marks, three questions of 3 marks and 2 questions of 4 marks. You have to attempt only one of the alternatives in all such questions.

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.

Submitted By Mr. Hemant Kumar
Delhi Public School , Mathura Refinery Nagar, Mathura
Email Id : [email protected]