Time allowed : 3 hours Maximum Marks : 80 3 … observer 1.5m tall is 28.5m away from a chimney. The angle of elevation of the top of a chimney from her eye is 45 . What is the height

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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)

MA 2043

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SECTION – A /

Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 – 10, four

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

1 10 1

1. The roots of the quadratic equation x23x2=0

(A) (1,2) (B) (1, 2) (C) (1,2) (D) (1,2)

x23x2=0

(A) (1,2) (B) (1, 2) (C) (1,2) (D) (1,2) 2. In an A.P if a=5, d=2.5, an=7.5, then n is

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

A.P a=5, d=2.5, an=7.5 n

(A) 1 (B) 2 (C) 3 (D) 4 3. If radii of two concentric circle are 13cm and 12cm. Then the length of chord of one circle

which is tangent to the other circle is :- (A) 4 cm (B) 5 cm (C) 10 cm (D) 12 cm

13cm 12cm

(A) 4 cm (B) 5 cm (C) 10 cm (D) 12 cm 4. In given figure, if PQR is a tangent to a circle at Q whose centre is O, Ab is a chord parallel to

PR and BQR=50 then AQB is equal to :-

(A) 80 (B) 40 (C) 20 (D) 50

O Q PQR AB, PR

BQR=50 AQB

(A) 80 (B) 40 (C) 20 (D) 50



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5. In the figure if AOB=1100, then APB is equal to :-

(A) 110 (B) 35 (C) 55 (D) 70

AOB=1100, APB

(A) 110 (B) 35 (C) 55 (D) 70

6.

If a similar triangle whose sides are 3

5 times the corresponding sides of a given triangle is to

be constructed, the point on the side of a given triangle divides the side in the ratio is : (A) 3 : 2 (B) 2 : 3 (C) 3 : 5 (D) 5 : 3

3

5

(A) 3 : 2 (B) 2 : 3 (C) 3 : 5 (D) 5 : 3 7. The volume and base radii of a cone and a hemisphere are equal, then the ratio of height of

cone and radius is :- (A) 1 : 3 (B) 1 : 2 (C) 2 : 3 (D) 2 : 1

(A) 1 : 3 (B) 1 : 2 (C) 2 : 3 (D) 2 : 1 8. The area of a circle is 154cm2, then its circumference is :

(Use = 22

7)

(A) 44 cm (B) 22 cm (C) 88 cm (D) 176 cm

154cm2

(Use = 22

7)

(A) 44 cm (B) 22 cm (C) 88 cm (D) 176 cm

9.

The shadow of a tower 100m high is 100

3m. The angle of elevation of sun is

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

100m. 100

3m.

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



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10. A die is thrown once. The probability of getting even number less than 5 is

(A) 1

2 (B)

1

3 (C)

1

6 (D)

2

3 5

(A) 1

2 (B)

1

3 (C)

1

6 (D)

2

3

SECTION – B

Question numbers 11 to 18 carry 2 marks each.

11 18 2

11. For what value of K, the roots of the quadratic equation 3x22xk=0 are real and equal ?

K 3x22xk=0

12. Which term of A.P : 17, 14, 11, ------------- is 43 ?

A.P : 17, 14, 11, ------------- 43

13. Prove that the tangents drawn at the end points of a diameter of a circle are parallel.

14. For each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in fig. Find the area of the remaining portion of the

square. (use = 3.14)

4 cm 1 cm 2 cm

(use = 3.14)



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15. A metallic sphere of radius 6 cm is melted and recast into the shape of a cylinder of radius 3 cm. Find the height of the cylinder.

6 cm 3 cm

16. Find the point on x-axis which is equidistant from the points (2, 5) and (2, 9).

x- (2, 5) (2, 9)

17. Find the ratio in which the point (2, y) divide the line segment joining the points A

(2, 2) and B (3, 7). Also find the value of y.

A (2, 2) B (3, 7) (2,y) y

18. Find the probability of getting 53 Fridays in a leap year.

53

OR

Two dice are thrown simultaneously at the same time. Find the probability of getting different number on both the dice.

SECTION – C


19 28 3

19. Find the roots of the given equation :-

1

2 1

x

x

2 1

1

x

x

5

2 : x 1,

1

2

1

2 1

x

x

2 1

1

x

x

5

2 : x 1,

1

2

OR

A natural number when increased by 12, becomes equal to 160 times reciprocal of given natural number. Find the number.

12 160

20. The sum of the 4th and 8th terms of an A.P is 24 and the sum of the 6th and 10th term is 44. Find

the first three terms of the A.P.

A.P 24 44 A.P.

21. In fig common tangents AB and CD to two circles with centre O and O " intersect in E. Prove

that AB=CD.



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O O" AB CD E

AB=CD.

OR

ABC is an isosceles triangle with AB=AC. If the incircle of ABC touches the sides AB, BC and CA at D, E and F respectively, Show that E bisects BC.

ABC AB=AC ABC AB, BC

CA D, E F E, BC

22. Draw a triangle ABC with sides BC=7 cm, B=450, A=1050. Then construct another triangle

whose sides are 3

4 times the corresponding sides of ABC.

ABC BC=7 cm, B=450 A=1050

ABC 3

4

23. In the fig. a square OABC of side 20 cm is inscribed in a quadrant OPBQ. Find the area of

shaded region.

OPBQ OABC 20cm

24. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of

the cone is 2 cm and the diameter of the base of cone and hemisphere is 4 cm. Find the

volume of toy so formed. (Use = 3.14)

2 cm

4 cm ( = 3.14 )

OR



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A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 cm of uniform thickness. Find the thickness of the wire.

1cm 8cm 18 cm

25. An observer 1.5m tall is 28.5m away from a chimney. The angle of elevation of the top of a

chimney from her eye is 45. What is the height of the chimney.

1.5 m 28.5m

45

26. Find the value of ‘K’ for which the points with co-ordinates. (7,2), (5,1) and (3,K) are

collinear.

‘K’ (7,2), (5,1) (3,K)

27. Show that the points with coordinates (1,7), (4,2), (1,1) and (4,4) are the vertices of a

square.

(1,7), (4,2), (1,1) (4,4)

28. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is four times that of a red ball. Find the number of blue balls in the bag.

5

4

SECTION – D


29 34 4

29. In a flight of 600km, an aircraft was slowed down due to bad weather. Its average speed for

the trip was reduced by 200km/hr. and the time increased by 30 minutes. Find the duration of flight.

600 km,

200km/hr. 30

OR

Find two consecutive odd positive integers, sum of whose square is 290.

290

30. Find the sum of all integers between 200 and 300 that are divisible by 7.

200 300 7

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

32. A tent is in the shape of a right circular cylinder upto a height of 3m and conical above it. The total height of the tent is 13.5m and radius of base 14m. Find the cost of cloth required to make the tent at the rate of Rs.80/- per sq.metre.

3m 13.5m

14m 80



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OR

A cylinder of radius 12cm contains water to a depth of 20cm. A spherical solid iron ball is dropped in the cylinder and thus the level of water is raised by 6.75cm. Find the diameter of the ball.

12cm 20cm.

6.75cm.

33. A sphere of radius 8cm is dropped in a right circular cylinder vessel partly filled with water.

The diameter of the vessel is 16cm. If the sphere is completely submerged in water, by how much will the level of water rise in the vessel.

8cm 16

cm

34. An aeroplane when 3000m high passes vertically above another aeroplane at an instant when

the angle of elevation of aeroplanes at the same observation points are 60 and 45 respectively. How much high is the one plane than the other ?

3000m

60 45

- o O o -



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Time allowed : 3 hours Maximum Marks : 80 3 … observer 1.5m tall is 28.5m away from a chimney. The angle of elevation of the top of a chimney from her eye is 45 . What is the height