summative assessment ii, 2012 65021

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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)

65021

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SECTION–A /

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

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

1 10 1

1. Which of the following is a quadratic equation ?

(A) (x3) (x1)x24 x9 (B) (x3) (2x1)x (x5)

(C) x23x1(x2)2 (D) (x1)2x (x3)

(A) (x3) (x1)x24 x9 (B) (x3) (2x1)x (x5)

(C) x23x1(x2)2 (D) (x1)2 x (x3)

2. (3k2), (5k3) and (4k7) are 3 consecutive terms of an A.P. Then the value of k is :

(A) 52 (B) 10 (C) 5 (D) 5

(3k2), (5k3) (4k7) 3 k

(A) 52 (B) 10 (C) 5 (D) 5

3. In given figure PT and PR are two tangents to a circle with centre O, such that

ROT135, then the measure of TPR is :

(A) 90 (B) 45 (C) 120 (D) 240

PT PR O ROT135 TPR

(A) 90 (B) 45 (C) 120 (D) 240

4. If the radii of two concentric circles are 24 cm and 26 cm respectively, then the length of each chord of one circle which is tangent to the other circle is : (A) 5 cm (B) 10 cm (C) 20 cm (D) 25 cm


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24 cm 26 cm

(A) 5 cm (B) 10 cm (C) 20 cm (D) 25 cm 5. PQ and PR are two tangents to the circle with centre O, from an external point P. If radius

of the circle is 8 cm, the length of the tangents is 10 cm, then the measure of OP is :

(A) 2 41 cm (B) 6 cm (C) 18 cm (D) 2 cm

O P PQ PR

8 cm 10 cm OP

(A) 2 41 cm (B) 6 cm (C) 18 cm (D) 2 cm

6. To draw a pair of tangents to a circle which are inclined to each other at an angle of 45, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be : (A) 90 (B) 135 (C) 180 (D) 145

45

(A) 90 (B) 135 (C) 180 (D) 145 7. The ratio of the total surface area of a solid hemisphere to the square of its radius is :

(A) 2 : 1 (B) 3 : 1 (C) 4 : 1 (D) 1 : 4

(A) 2 : 1 (B) 3 : 1 (C) 4 : 1 (D) 1 : 4 8. In the given figure, AP12 cm and PB16 cm. Taking the value of as 3, the perimeter of

the shaded region is :

(A) 48 cm (B) 58 cm (C) 64 cm (D) 88 cm

AP12 cm PB16 cm 3

(A) 48 cm (B) 58 cm (C) 64 cm (D) 88 cm

9 The length of the shadow of a vertical pole is 3 times its height, the Sun’s altitude is :

(A) 90 (B) 45 (C) 60 (D) 30

3

(A) 90 (B) 45 (C) 60 (D) 30 10 In a throw of a pair of dice, the probability of getting a doublet is :

(A) 1

2 (B)

1

3 (C)

1

6 (D)

5

12

(A) 1

2 (B)

1

3 (C)

1

6 (D)

5

12


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SECTION-B /

Question numbers 11 to 18 carry two marks each.

11 18 2

11. If the equation kx25xk0 has equal roots, find the value of k.

k kx25xk0

12. Find the value of a, b and c, such that the numbers a, 10, b, c, 31 are in A.P.

a, b c a, 10, b, c, 31

13. In the given figure BOA is a diameter of a circle and the tangent at a point P meets BA

produced at T. If PBO30, what is the measure of PTA ?

BOA P BA T

PBO30 PTA

14. Calculate the area of the minor segment of the circle, made by a chord which subtends a

right angle at the centre of a circle of radius 12 cm. (Use 3.14.)

12 cm 90

(3.14

15 A metallic sphere of total volume is melted and recast into the shape of a right circular cylinder of radius 0.5 cm. What is the height of cylinder ?

0.5 cm

16 Find the midpoint of side BC of ABC, with A (1, 4) and the midpoints of the sides through A being (2, 1) and (0, 1).

ABC BC A (1, 4) A

(2, 1) (0, 1)

17 Name the type of triangle PQR formed by the points

2 , 2 , 2 , 2 , 6 , 6P Q R

2 , 2 , 2 , 2 , 6 , 6P Q R PQR

18 A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of the red ball, find the number of blue balls in the bag.

5


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OR/

There are 30 cards of the same size in a bag in which the numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3.

30 1 30

3

SECTION-C /

Question numbers 19 to 28 carry three marks each.

19 28 3

19. Find the roots of the following :

1 2 1 1 2 , , 1

2 1 1 2

x xx

x x

1 2 1 1 2 , , 1

2 1 1 2

x xx

x x

OR/

In a class test, the sum of the marks obtained by a student in Mathematics and Science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science, the product of the marks would have been 180. Find his marks in two subjects.

28 3

4 180

20. How many multiples of 4 lie between 11 and 266 ?

11 266 4

21. A circle is inscribed in a ABC, with the sides AB, BC and AC as 8 cm, 10 cm and 12 cm respectively. Find the lengths of AD, BE and CF

ABC AB, BC AC 8 cm, 10 cm 12 cm

AD, BE CF

OR/

Prove that the tangents at the ends of a chord of a circle make equal angles with the chord.


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22. Construct tangents to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.

4 cm 6 cm

23. In the given figure AB is the diameter of the larger semicircle. AB21 cm, AMMNNB.

Semicircles are drawn with AM, MN and NB as shown. Using 22

7 , calculate the area

of the shaded region.

AB AB21 cm AMMNNB AM, MN NB

22

7

24. The radii of two right circular cylinders are in the ratio of 2 : 3 and their heights are in the

ratio of 5 : 4. Calculate the ratio of their curved surface areas and ratio of their volumes.

2 : 3 5 : 4

OR /

A toy is in the form of a cone mounted on a hemisphere of common base of diameter 7 cm.

If the height of the toy is 15.5 cm, find the total surface area of the toy 22

Take7

.

7 cm

15.5 cm 22

7

.

25 A tree breaks due to storm and broken part bends, so that the top of the tree touches the ground making an angle of 30 with the ground. The distance from the foot of the tree to the point where the top touches the ground is 8 metres. Find the height of the tree before it was broken.

30 8

26 If (a, b) is the midpoint of the line segment joining the points A (10, 6) and B (k, 4) and a2 b18, find the value of k and the distance AB.

A (10, 6) B (k, 4) (a, b) a2 b18 k

AB

27 Find the ratio in which the line 2x3y50 divides the line segment joining the points (8, 9) and (2, 1). Also find the co-ordinates of the point of division.

2x3y50 (8, 9) (2, 1)

28 Three unbiased coins are tossed together. Find the probability of getting


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(i) at least two heads (ii) at most two heads.

(i)

(ii)

SECTION-D /

Question numbers 29 to 34 carry four marks each.

29 34 4

29. Solve for x : 9x26 a2 x(a4b4)0

x 9x26 a2 x(a4b4)0

OR/

The perimeter of a rectangular field is 82 m and its area is 400 square meters. Find the

length and breadth of the rectangle.

82 400

30. The sum of the 3rd and 7th terms of an AP is 6 and their product is 8. Find the sum of first 20 terms of the A.P.

6 8 20

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

32. A rectangular sheet of paper of dimensions 44 cm18 cm is rolled along its length and a

cylinder is formed. Find the volume of the cylinder so formed (use 22

7)

44 cm18 cm

( 22

7 )

OR /

A solid right circular cylinder has a total surface area of 462 sq. cm. Its curved surface area

is one-third of its total surface area. Find the volume of the cylinder (use 22

7)

462

1

3 (

22

7)

33. An open container made up of a metal sheet is in the form of a frustum of a cone of height 7 cm with radii of its lower and upper circular ends as 4 cm and 10 cm respectively. Find the cost of oil which can completely fill the container at the rate of Rs. 50/litre.

(Take 22

7)

7 cm

4 cm 10 cm 50 /


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(22

7)

34. From, a point P on the ground the angle of elevation of the top of a 10 m tall building is 30. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag staff from P is 45. Find the length of the flag staff ; and the distance of building from point

P 3 1.732

P 10 30

P 45 P

3 1.732

- o 0 o -


summative assessment ii, 2012 65021

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