Variation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

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Question No: #61

The cost of a hostel is partly constant and partly proportional to the number of people staying in that hostel. If the number of people is 120 the cost is Rs 2000 and if the number of people is 100 the cost is Rs 1700. If the cost is 1880 rupees, find the number of people.
Ans: 112
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Question No: #62

The volume of a sphere varies directly as the cube of its radius. Three inert spheres with diameters of 1½, 2 and 2½ meters were melted and a new inert sphere was prepared. What is the diameter of the new sphere?
Ans: 3 meter
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Question No: #63

The volume of a cone varies jointly as the square of its radius and its height. If the ratio of the radii of two cones is 3:4 and the ratio of their heights is 6:5, find the ratio of their volumes.

Question No: #64

If 15 farmers can cultivate 18 bighas of land in 5 days, then calculate by using the theory of variation the number of days required by 10 farmers to cultivate 12 bighas of land.
Ans: 5 days
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Question No: #65

The volume of a sphere is proportional to the cube of its radius and the surface area of ​​a sphere is proportional to the square of its radius. Show that the square of the volume of a sphere is proportional to cube of its surface area.

Question No: #66

The period of oscillation of a simple oscillator is linearly proportional to the square root of its length. If the period of oscillation of a pendulum 100 cm long is 2 seconds, find the length of the pendulum whose period of oscillation is 3 seconds.
Ans: 225 cm
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Question No: #67

The distance traveled by a freely falling heavy object from rest is directly proportional to the square of the time of the fall up to that distance. If the object falls a distance of 64 meters in 2 seconds, what distance will the object fall in tenth second?
Ans: 304 m
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Question No: #68

The price of a precious gem is directly varies to square of its weight. This gem is broken into four pieces and the ratio of weight of those pieces are `1:2:3:4`; If the amount of loss is Rs 70,000, then find out the price of original gem.

Question No: #69

A valuable piece of stone whose price is rs 15600 breaks into three pieces whose weights are in the ratio `2:3:5` . If the value of the stone varies as the cube of its weights , find the percentage of loss due to breaking .
Ans: 84%
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