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Important Instructions for the

School Principal

(Not to be printed with the question paper)

1) This question paper is strictly meant for the use in School Based Summative Assessment-

II, March-2012 only. This question paper is not to be used for any other purpose except

mentioned above under any circumstances.

2) The intellectual material contained in the question paper is the exclusive property of

Central Board of Secondary Education and no one including the user school is allowed to

publish, print or convey (by any means) to any person not authorised by the Board in this

regard.

3) The School Principal is responsible for the safe custody of the question paper or any other

material sent by the Central Board of Secondary Education in connection with School

based SA-II, March-2012, in any form including the print-outs, compact-disc or any other

electronic form.

4) Any violation of the terms and conditions mentioned above may result in the action

criminal or civil under the applicable laws/byelaws against the offenders/defaulters.

Note: Please ensure that these instructions are not printed with the question

paper being administered to the examinees.

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SUMMATIVE ASSESSMENT – II, 2012

II, 2012

MATHEMATICS /

Class – X / X

Time allowed : 3 hours Maximum Marks : 80

3 80

General Instructions :

(i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A, B, C and D.

Section-A comprises of 10 questions of 1 mark each, Section-B comprises of 8 questions of 2

marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises

of 6 questions of 4 marks each.

(iii) Question numbers 1 to 10 in Section-A are multiple choice questions where you are to select

one correct option out of the given four.

(iv) There is no overall choice. However, internal choices have been provided in 1 question of

two marks, 3 questions of three marks each and 2 questions of four marks each. You have to

attempt only one of the alternatives in all such questions.

(v) Use of calculator is not permitted.

(i)

(ii) 34 10

1 8 2 10

3 6 4

(iii) 1 10

(iv) 2 3

3 4 2

(v)

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SECTION–A /

Question numbers 1 to 10 carry one mark each. For each questions, four alternative

choices have been provided of which only one is correct. You have to select the correct choice.

1 10 1 4

1. Which of the following equations has

1

5 as a root ?

(A) 35x22x10 (B) 2x27x60 (C) 10x23x10 (D) 35x212x10

1

5

(A) 35x22x10 (B) 2x27x60 (C) 10x23x10 (D) 35x212x10

2. If 18, x, y, 3 are in A.P., then value of xy is :

(A) 12 (B) 15 (C) 16 (D) 11

18, x, y, 3 xy

(A) 12 (B) 15 (C) 16 (D) 11 3. A quadrilateral PQRS is drawn to circumscribe a circle. If PQ, QR, RS (in cm) are 5, 9, 8

respectively, then PS (in cm) equals : (A) 7 (B) 6 (C) 5 (D) 4

PQRS PQ, QR RS cm 5, 9 8

cm PS

(A) 7 (B) 6 (C) 5 (D) 4 4. If two tangents inclined at an angle 60 are drawn to a circle of radius 5 cm, then length of

each tangent (in cm) is equal to :

(A) 5 3

2 (B) 10 (C) 3 (D) 5 3

5 cm 60

cm

(A) 5 3

2 (B) 10 (C) 3 (D) 5 3

5. In the given figure, the pair of tangents PQ and PR drawn from an external point P to a

circle with centre O are inclined to each other at 90. If length of each tangents is 5 cm, then the radius (in cm) of the circle is :

(A) 10 (B) 7.5 (C) 5 (D) 2.5

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O P PQ PR

90 5 cm cm

(A) 10 (B) 7.5 (C) 5 (D) 2.5

6. To draw a pair of tangents to a circle which are inclined to each other at an angle of 30, it is

required to draw tangents at end points of two radii of the circle, the angle between which should be : (A) 30 (B) 60 (C) 120 (D) 150

30

(A) 30 (B) 60 (C) 120 (D) 150 7. The ratio of the volume of two spheres is 8 : 27. If r and R are the radii of spheres

respectively, then (Rr) : r is (A) 1 : 2 (B) 1 : 3 (C) 2 : 3 (D) 4 : 9

8 : 27 r R (Rr) : r

(A) 1 : 2 (B) 1 : 3 (C) 2 : 3 (D) 4 : 9 8. The area (in cm2) of the circle that can be inscribed in a square of side 8 cm is :

(A) 64 (B) 16 (C) 8 (D) 32

8

(A) 64 (B) 16 (C) 8 (D) 32 9. If two towers of height h1 and h2 subtend angles of 60 and 30 respectively at the

mid-point of the line joining their feet, then h1 : h2 is :

(A) 3 : 1 (B) 3 : 1 (C) 1 : 3 (D) 1 : 3

h1 h2 60

30 h1 : h2

(A) 3 : 1 (B) 3 : 1 (C) 1 : 3 (D) 1 : 3

10. In tossing a die, the probability of getting an odd number or a number less than 4 is :

(A) 1 (B) 1

2 (C)

2

3 (D)

3

4 4

(A) 1 (B) 1

2 (C)

2

3 (D)

3

4

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SECTION-B /

Question numbers 11 to 18 carry two marks each.

11 18 2

11.

Find the roots of the quadratic equation : 2111 1 0

3x x

21

11 1 03

x x

12. Which term of A.P. : 21, 18, 15, …….. is zero ?

21, 18, 15, ……..

13. In the given figure, tangents AC and AB are drawn to a circle from a point A such that

BAC30. A chord BD is drawn parallel to the tangent AC. Find DBC.

A AC AB

BAC30 AC BD DBC

14. In the given figure, O is the centre of the circle. Find the area of shaded region, given that BC4 cm and AC3 cm.

O BC4 cm

AC3 cm

15. Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resultant cuboid.

64 cm3

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16. If the points A(1, 2), B(4, q), C(p, 6 ) and D(3, 5), are the vertices of a parallelogram ABCD,

find the values of p and q.

A(1, 2), B(4, q), C(p, 6 ) D(3, 5) ABCD p q

17. Find the ratio in which the line segment joining the points X(1, 5) and Y(4, 5) is divided

by the x-axis.

X(1, 5) Y(4, 5) x-

18. A number x is selected from the numbers 1, 2, 3 and then a second number y is selected

from the numbers 1, 4, 9. What is the probability that the product xy of the two numbers will be less than 9 ?.

1, 2, 3 x 1, 4, 9 y

xy 9

OR/

Two dice are thrown at the same time. Find the probability of getting a multiple of 3 on first and multiple of 2 on the other die.

3 2

SECTION-C /

Question numbers 19 to 28 carry three marks each.

19 28 3

19.

Solve for x : 1 2

3 ; 1 21 2

x xx ,

x x

x 1 2

3 ; 1 21 2

x xx ,

x x

OR/

Solve for x :

1 1 1 10 0 0; a , b , c

a b x a b x

and abx ≠ 0

x : 1 1 1 1

0 0 0; a , b , ca b x a b x

and abx ≠ 0

20. How many terms of the A.P. : 15, 13, 11, …. are needed to make the sum 55 ?

Explain the reason for double answer ?

15, 13, 11, …. 55

21. In the given figure a circle touches the sides PQ, QR and PR of PQR at the points X, Y and

Z respectively. Show that PXQYRZ XQYRZP1

2 (Perimeter of PQR)

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PQR PQ, QR PR X, Y Z

PXQYRZ XQYRZP1

2 PQR

OR/

In the given figure, from an external point P, tangents PX and PY are drawn to a circle with centre O. If AB is another tangent to the circle at C and PX14 cm, find the perimeter of PAB.

O P PX PY

C AB PX14 cm PAB

22. Draw a ABC in which CA6 cm, AB5 cm and BAC45. Then construct a triangle

similar to the triangle ABC whose sides are 3

5 of the corresponding sides of the triangle

ABC.

ABC CA6 cm AB5 cm BAC45

ABC 3

5

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23. In the given figure, PQR is an equilateral triangle of side 8 cm and P, Q, R are centres of circular arcs, each of radius 4 cm. Find the area of shaded region. (Use 3.14 and

3 1.732)

PQR 8 cm P, Q R

4 cm 3.14

3 1.732

24. How many coins 1.75 cm in diameter and of thickness 2 mm must be melted to form a

cuboid of dimensions 11 cm10 cm7 cm ?

11 cm10 cm7 cm 1.75 cm 2 mm

OR/

A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is exactly half submerged in water, by how much will the level of water rise in the cylindrical vessel.

6 cm 12 cm

25. Two men on the same side of the tower and in the same straight line with its base notice

the angle of elevation of the top of the tower to be 30 and 60. If the height of the tower is 150 m, find the distance between the two men.

30 60 150 m

26. If the coordinates of points A and B are (2, 2) and (2, 4) respectively, find the

coordinates of a point X such that 3

AX7

AB and X lies on the line segment AB.

A B (2, 2) (2, 4) X

3AX

7 AB X AB

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27. Find the area of the triangle formed by joining the mid-points of the sides of the triangle ABC whose vertices are A(0, 1), B(2, 1), C(0, 3). Find the ratio of this area to the area of the given triangle ABC.

ABC A(0, 1), B(2, 1) C(0, 3)

ABC

28. Cards marked with numbers 13, 14, 15, ……, 60 are placed in a box and mixed thoroughly.

One card is drawn at random from the box. Find the probability that the sum of digits on the card drawn is 5.

13, 14, 15, ……, 60

5

SECTION-D /

Question numbers 29 to 34 carry four marks each.

29 34 4

29. A shopkeeper buys a number of packets of biscuits for Rs. 80. If he had bought 4 more packets for the same amount, each packet would have cost Re. 1 less. How many packets did he buy ?

80 4

1

OR/

The difference of two number is 5 and the difference of their reciprocals is

1

10. Find the

numbers.

5 1

10

30. Find the sum of all numbers between 250 and 1000 which are exactly divisible by 3.

250 1000 3

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

32. A decorative block is made of two solids – a cube and a hemisphere. The base of the block is the cube with edge of 7 cm and the hemisphere attached on the top has a diameter of 4.9 cm. If the block is to be painted, find the total area to be painted.

7 cm

4.9 cm

OR/

A godown is in the form as shown in the figure. The vertical cross-section parallel to the width side of the building is a rectangle of size 7 m3 m mounted by a semicircle of radius 3.5 m. The inner measurements of the cubidal portion are 10 m7 m3 m. Find the volume of the godown.

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7 m 3 m

3.5 m

10 m7 m3 m

33. A turks cap is shaped like a frustum of a cone. If its radius on the open side is 10 cm,

radius at the upper base is 4 cm and its slant height is 15 cm, find the area of the material used for making it.

10 cm

4 cm 15 cm

34. From the top of a building 60 m high, the angles of depression of the top and bottom of a

vertical lamp post are observed to be 30 and 60 respectively, Find the height of the lamp

post. (Take 3 1 732. )

60 m 30 60

3 1 732.

- o O o -

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