SECTION-I
1. The length of the longest stick that can be fitted in a cubical vessel of edge 20 cm long is _________.
(a) 20√3 cm (b) 20√2 cm (c) 20 cm (d) 40 cm
2. A matchbox measures 6 cm x 2 cm x 1.5 cm. The volume of packet containing 5 such boxes is _________.
(a) 80 cm3 (b) 180 cm3 (c) 90 cm3 (d) 100 cm3
3. The volume of cone of radius ‘r/2’ and height ‘2h’ is ______________.
(a) 1/3 πr2h (b) ) 1/4 πr2h (c) ) 1/5 πr2h (d) ) 1/6 πr2h
4. The radii of two cylinders are in the ratio 2:3 and the heights are in the ratio 5:3. The ratio of their
volume is ___________.
(a) 4:9 (b) 9:4 (c) 20:27 (d) 27:20
5. In an experiment a coin is tossed 500 times. If head turns up 280 times, then the probability of getting a
tail is ___________.
(a) 14/25 (b) 11/25 (c) 13/25 (d) 19/25
6. In a pack of playing cards, the number of face cards are ________.
(a) 4 (b) 12 (c) 13 (d) 26
7. Which of the following cannot be the probability of an event?
(a) 0 (b) 1/5 (c) 5/4 (d) 1
SECTION-II
CASE STUDY QUESTION-1
8. 50 plants were planted in each school out of 10 schools. After a month, the number of plants that
survived are given below:
School 1 2 3 4 5 6 7 8 9 10
No. of plants survived 40 35 32 45 35 30 45 40 35 25
Based on the above informations, answer the following:
(i) What is the probability of survival of more than 40 plants in a school?
(a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5
(ii) What is the probability of survival of less than 35 plants in a school?
(a) 7/10 (b) 1/10 (c) 3/10 (d) 9/10
(iii) What is the probability of survival of exactly 32 plants in a school?
(a) 3/10 (b) 7/10 (c) 9/10 (d) 1/10
(iv) What is the probability of survival of more than 35 plants in a school?
(a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5
CASE STUDY QUESTION-2
9. On his birthday in the month of January, Dev distributed soup. He stored the soup in a cylindrical
bucket of base radius 2 cm and height 98 cm. He distributed the oup in a hemispherical bowl of radius
7 cm to the poor people and also gave a blanket to them.
Based on the above details, answer the following:
(i) What is the volume of the cylindrical bucket?
(a) 392π cm3 (b) 292 π cm3 (c) 398 π cm3 (d) 298 π cm3
(ii) How many people were served with soup?
(a) 15 (b) 18 (c) 12 (d) 20
(iii) What is the inner surface area of hemispherical bowl?
(a) 368 cm2 (b) 308 cm2 (c) 208 cm2 (d) 298 cm2
(iv) How many blankets did Dev need?
(a) 10 (b) 12 (c) 22 (d) 15
SECTION-III
10. The height of a cone is 12 cm. If its volume is 100 π cm3, find its slant height.
11. The dome of a building is in the form of a hemisphere of radius 6.3 m. Find the cost of painting at the
rate of Rs.16/100m2.
12. In a survey of 400 youngsters aged 16-20 years, it was found that 191 had their voter ID-card. If an
adult is selected at random, find the probability that he/she doesn’t have his/her voter ID- card.
SECTION-IV
13. The LSA of a cube is 576 m2. Find its volume and TSA.
14. The circumference of the base of a right circular cone is 44√7 cm and its slant height is 28 cm. Find
the volume of the cone.
15. The weights of 60 persons in a group are given below.
Weight in kg 60 61 62 63 64 65
No. of persons 5 18 4 16 5 12
Find the probability that a person selected at random has
(i) weight less than 65 kg
(ii) weight between 61kg and 64 kg
(iii) weight between greater than or equal to 64 kg
SECTION-V
16. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The
diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is
14 cm, find the volume of the wood and that of the graphite.
17. A survey found that ages of 250 workers in a factory is distributed as follows:
Ages(in years) No. of workers
20-29 50
30-39 35
40-49 95
50-59 55
60 and above 15
If a person is selected at random, find probability that the person is :
(i) 40 years or more
(ii) having age from 30 to 39 years
(iii) under 60 but over 39 years
(iv) 30 years or more
(v) having age from 50-59 years
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