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Section - A

1. A quadratic equation whose one root is 3 and the sum of the roots is 0, is

(a) x2 + 3 = 0 (b) x2 + 9 = 0

(c) x2 - 9 = 0 (d) x2 - 3 = 0

2. The next term of the AP 8 , 18 , 32 ... is

(a) 65 (b) 60

(c) 50 (d) 55

3. The distance of the point (3, -4) from the y-axis is

(a) 7 units (b) 6 units

(c) 3 units (d) 4 units

4. To draw a pair of tangents to a circle which are inclined to each other at an angle x, it is

draw tangents at the end points of those two radii of the circle, the angle between which is

(a) 90 - x (b) 90 + x

(c) 180 - x (d) 180 + x

5. The sum of n terms of the series 3 12 27 18 ...+ + + + is

(a)

2n(n 1)

3

+

(b)

3n(n 1)

2

-

(c)3n (n 1)

2

+(d)

2n(n 1)

3

-

6. The famous mathematician associated with finding the sum of first 100 natural numbers is

(a) Euclid (b) Newton

(c) Gauss (d) Pythagoras

Sample Paper(Based on CBSE CCE SA - 2)

(X) MATHEMATICS

[Time allowed: 3 hours] [Maximum

General Instructions:

1. All questions are compulsory.

2. The question paper consists of 34 questions divided into 4 sections, section A, B, C, and D.

3. Section A contains 10 multiple choice type questions of 1 mark each. Section B contains 8 qu

marks each, section C contains 10 questions of 3 marks each and section D contains 6 que

marks each.

4. There is no overall choice. However, internal choice has been provided in 1 question of tw

questions of three marks each and 2 questions of four marks each. Attempt only one of the a

in all such questions.

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Section - D

29. 6500 were divided equally among a certain number of persons. Had there been 15 more persons, each

would have got 30 less. Find the original number of persons.

OR

One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to the

mountains and 15 camels were on the bank of the river. Find the number of camels.

30. Find the sum of all natural numbers between 200 and 1502 which are exactly divisible by 3.

31. Prove that the lengths of tangents drawn from an external point to a circle are equal.

32. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter aof the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

a

a

OR

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere

as shown in the figure. The external diameters of the frustum are 5 cm and 2 cm and the height of the

entire shuttle cock is 7 cm. Find its external surface area.

5 cm

7 cm

2 cm

33. The middle portion of a wooden rolling pin (belan) is a cylinder of diameter 6 cm with hemispherical

ends of same diameter. Two cylindrical rods, each of length 9 cm and diameter 2 cm are attached on

either side of the hemispherical ends. If the total length of the rolling pin is 42.5 cm, find its volume.

Also, compute its mass if 1 cubic cm of wood has a mass of 0.9 grams.

6cm

42.5 cm

9 cm2 cm

34. The angle of elevation of the top of an unfinished tower at a point 120 m from its base is 45. How muchmust the tower be raised so that the angle of elevation at the same point be 60?

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7. A cylindrical pencil sharpened at one edge is the combination of

(a) two cylinders (b) frustum of a cone and a cylinder

(c) a hemisphere and a cylinder (d) a cone and a cylinder

8. If the radius of the wheel is 49 cm, then the number of times the wheel will rotate in a journey of 2002 m

is

(a) 1300 (b) 650

(c) 1000 (d) 1500

9. If the diameter of a protractor is 14 cm, then its perimeter is

(a) 24 cm (b) 36 cm

(c) 48 cm (d) 60 cm

10. The given figure shows the observation of point C from point A. The angle of depression from A isA

B

2 m

C2 3 m

(a) 60 (b) 30

(c) 45 (d) 75

Section - B

11. Find the roots of the quadratic equation: 21x2 - x - 2 = 0.

12. AP is a tangent to the circle with centre O such that OP = 4 cm andOPA = 30. Find AP

4 cm

O

A P30

13. The minute hand of a clock is 21cm long. Find the area described by the minute hand on the face of

the clock between 7 : 00 am and 7 : 05 am.

14. A cuboidal box of dimensions 16 cm 8 cm 8 cm contains glass spheres of diameter 6 cm. If 119.68 cm3

of space remains vacant, find the number of glass spheres. [Take = 3.14]

15. Line segment PQ is divided into five equal parts at A, B, C and D. If A is (-3, -7) and C is (1, 1), find the

coordinates of P, B, D and Q.

16. If A(1, 2), B(4, y), C(x, 6) and D(3, 5) be the vertices of a parallelogram taken in order, find x and y.

17. Two dice are thrown at the same time. Find the probability of getting a doublet of odd.

OR

A coin is tossed two times. Find the probability of getting at least one head.

18. The first term of an A.P is 4 and the last term is 61. The sum of all these terms is 650. Find the common

difference.

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Section - C

1 9. Solve: 3 6x2 - 12ax + (a2 - b2) = 0

OR

Solve:x 1x 34

, x 1and x 0x 1 x 15

++ = -

+

20. Find the sum of two middle most terms of the A.P1 15

1, , 0 ,.......2 2

- - .

21. From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is e

diameter of the circle, show that APB is equilateral.

22. From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is th

the circle at a point E and PA = 14 cm, find the perimeter of PCD.

A

C

E

DB

PO

23. AOB is a quadrant of a circle of radius 14 cm. From it, an equilateral OPQ is cut off as sh

figure. Calculate the area of the shaded part.22

Take 3 1.732,7

= p=

A Q

O

P

B

24. The rain water from a roof 22 m 20 m drains into a cylindrical vessel having diameter of b

height 3.5 m. If the vessel is just full, find the height of rainfall in cm.

OR

A well of diameter 3 m is dug 21 m deep. The earth taken out of it has been spread evenly a

to a width of 4 m to form an embankment. Find the height of the embankment.

25. From an aeroplane vertically above a straight horizontal plane, the angles of depression of two

kilometre stones on the opposite sides of the aeroplane are found to and. Show that the h

aeroplane, in kilometres istan . tan

tan tan

a b

a + b.

26. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

27. The end points of the diameter AOB of a circle C(O, r) are A(-3, 4) and B(3, -4). Find;(i) coordinates of its centre (ii) area of the circle

28. A class has 15 girls and 10 boys. The teacher calls on a student at random to answer a questi

in decimal form, the probability that a student called upon is

(i) a girl (ii) a boy

(iii) a student of the class (iv) the teacher of the class.