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CBSE Sample Paper-01

SUMMATIVE ASSESSMENT –II MATHEMATICS

Class – X

Time allowed: 3 hours Maximum Marks: 90

General Instructions:

a) All questions are compulsory.

b) The question paper consists of 31 questions divided into four sections – A, B, C and D.

c) Section A contains 4 questions of 1 mark each which are multiple choice questions, Section B

contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and

Section D contains 11 questions of 4 marks each.

d) Use of calculator is not permitted.

Section A

1. If P(E) = 0.07, then the probability of ‘not E’ is:

(a) 0 (b) 0.03 (c) 0.93 (d) 0.3

2. If A is a point on y − axis, whose ordinate os 3 and B is a point ( )5,2 ,− then the distance AB is:

(a) 26 units (b) 24 units (c) 5 units (d) 65

3. 12th term of the AP 5, 8, 11, 14, ….. is:

(a) 43 (b) 40 (c) 38 (d) 3

4. A 6 ft tall man finds that the angle of elevation of a 24 ft high pillar and the angle of depression

of its base are complimentary angles. The distance of the man from the pillar is:

(a) 4 3 m (b) 6 3 m (c) 8 3 m (d) 10 3

Section B

5. If the diameter of a semicircular protractor is 14 cm, then find its perimeter.

6. A heap of rice is in the form of a cone of radius 3 m and height 3 m. Find the volume of the rice.

How much cloth is required to just cover the heap?

7. A solid metallic hemisphere of radius 6 cm is melted and recasted into a right circular cone of

base radius 3 cm. Determine the height of the cone.

8. The graph of the polynomial 2y ax bx c= + + is shown in the figure. Write one value of 2 4 .b ac−

9. Find the sum of first 10 terms of the AP 10, 6, 2, ……..

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10. If ( )1 2 2 1,d d d d> be the diameters of two concentric circles and c be the length of a chord of a

circle which is tangent to the other circle, then prove that 2 2 22 1 .d c d= +

Section C

11. Find the ratio in which the line segment joining the points (6, 4) and ( )1, 7− is divided by x −

axis.

12. Three consecutive vertices of a parallelogram are ( ) ( )2, 1 , 1,0− − and ( )4,3 . Find the coordinates

of the fourth vertex.

13. In the given figure, sectors of two concentric circles of radii 7 cm and 3.5 cm are shown. Find

the area of the shaded region. 22

Use =7

π

14. The inner circumference of a circular track is 440 m. The track is 14 m wide. Find the diameter

of the outer circle of the track. 22

Use =7

π

15. Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80

cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will

the level of water rise in the tank in half an hour?

16. Find the value of k for which the roots of the quadratic equation 2 10 5 0kx x− + = are equal.

17. Find the 10th term from the end of the AP 8, 10, 12, …….., 126.

18. In the figure, if AB = AC, then prove that BE = EC.

19. A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole

observed from a point A on the ground is 60� and the angle of the depression of point A from

top of the tower is 45 .� Find the height of the tower. ( )Take 3 1.732=

20. 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, then find the number of blue balls in the bag.

Section D

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

Using the above result, prove the following:

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If a circle touches all the four sides of a quadrilateral ABCD, then prove that:

AB + CD = BC + DA

22. Draw a right triangle ABC, in which ∠ B = 90 ,� AB = 5 cm, BC = 4 cm. Then construct another

triangle A’BC’ whose sides are 5

3 times the corresponding sides of ∆ ABC.

23. A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at

random from the bag. What is the probability that the ball drawn is:

(i) white or blue? (ii) red or black?

(iii) not white? (iv) neither white nor black?

24. The vertices of a triangle are ( ) ( )1,3 , 1, 1− − and (5, 1). Find the lengths of medians through

vertices ( )1,3− and (5, 1).

25. A solid right circular cone of diameter 14 cm and height 8 cm is melted to form a hollow

sphere. If the external diameter of the sphere is 10 cm, then find the internal diameter of the

sphere.

26. A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the

base of the conical portion is 7 cm and the total height of the toy is 14.5 cm. Find the volume of

the toy.

27. Solve for :x 1 1 8 5, 0, 2,

2 2 5 2x

x x x

−+ = ≠− +

28. There are two windows in a house. A window of the house is at a height of 1.5 m above the

ground and the other window is 3 m vertically above the lower window. Ram and Shyam are

sitting inside the two windows. At an instant, the angle of elevation of a balloon from these

windows are observed as 45� and 30� respectively.

Read the above passage and answer the following questions:

(a) Find the height of the balloon from the ground.

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(b) Among Ram and Shyam, who is more closer to the balloon?

(c) Why windows are essential in any construction, commercial or residential?

(d) If the balloon is moving towards the building, then both angles of elevation will remain

same or not?

29. Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, then

find the sides of two squares.

30. The sum of three numbers in an AP is ( )3− and their product id 8. Find the numbers.

31. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a

point T. Find the length of TP.