**CBSE Sample Papers for Class 9 SA2 Maths Solved 2016 Set 10**

**SECTION – A**

Question numbers 1 to 4 carry 1 mark each.

1. A family contains father, mother, 1 male child and 3 female children. One of them is selected for trip to Jaipur, what is the probability that a female child is selected ?

2. A right circular cylinder just encloses a sphere of radius a cm, then find the curved surface area of the cylinder.

3. Find the number of planks of dimensions 4 m by 50 cm by 20 cm that can be stored in a pit which is 16 m long, 12 m wide and 4 m deep.

4. If the median of data arranged is ascending order 31, 33, 35, x, x + 10, 48, 48, 50 is 40, then find the value of x.

**SECTION – B**

Question numbers 5 to 10 carry 2 marks

7. A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimetres of iron has been used in making the tube ?

8. Find the sum of the deviations of the variate values 3, 4, 6, 8, 14 from their mean.

9. A cone, a hemisphere and a cylinder stand an equal bases and have the same height. Find the ratio of their volumes.

10. Find the median of 34, 32, x, x- 1, 19, 15, 11, where x is the mean of 10, 20, 30, 40,50.

**SECTION – C**

Question numbers 11 to 18 carry 3 marks each.

11. Three coins are tossed simultaneously 160 times with the following frequency of different outcomes :

12. Prove that the diagonals of a parallelogram divides it into two congruent triangles

17. A cube and cuboid have same volume. The dimensions of the cuboid are in the ratio 1 : 2 : 4. If the difference between the cost of polishing the cube and cuboid at the rate of Rs. 5 per m^{2} is Rs. 80, find their volumes.

18. Thirty children were asked about the number of hours they watched TV programmes in the previous week. The result was found as follows : 10, 6, 4, 2, 1, 3, 8, 3, 2, 3, 12, 5, 5, 2, 9, 6, 8, 12, 15, 8, 5, 7, 8, 1, 17, 4, 14, 6, 8, and 12.

(i) Construct a frequency distribution table for this data, taking class width 5 and one of the class as 5 – 10

(ii) How many children watched television for 15 or more than 15 hours a week ?

**SECTION – D**

Question numbers 19 to 28 carry 4 marks each.

19. Prove that the parallelogram on the same base and between the same parallels are equal in area.

23. Prove that angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

24. Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

26. Water flows at the rate of 5 m per minute through a cylindrical pipe, whose diameter is 7 cm. How long it will take to fill the conical vessel having base diameter 21m and depth 12 m ?

27. 30 plants were planted in each school out of 12 schools. After a month, the number of plants that survived are given below :

What is the probability of survival of :

(i) more than 20 plants in a school ?

(ii) less than 10 plants in a school ?

(iii) exactly 22 plants in a school ?

(iv) According to you what steps should be taken to save environment ?

**SECTION – E**

Question numbers 29 to 31 carry total of 10 marks based on the Open Text Theme provided by CBSE from Linear Equations in Two Variables.