Variation

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

Click on each question to see answer & solution.

Question No: #11

`x` varies directly as square of `y` and inversely as `z`. If `x=2` when `y=4` and `z=2`, then find the value of `y` when `x=3` and `z=3`.
Ans: `\pm 6`
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Question No: #12

If `(1/x - 1/y) \propto \frac{1}{x-y}`, then show that `(x^2+y^2) \propto xy`

Question No: #13

If `(1/x + 1/y) \propto \frac{1}{x+y}`, then show that `(x^2+y^2) \propto xy`

Question No: #14

If `(a+b) \propto \sqrt{ab}`, then show that `(\sqrt{a}+\sqrt{b}) \propto (\sqrt{a}-\sqrt{b})`.

Question No: #15

Given that, `A = B + C`, where `B \propto x^2` and `C \propto x^3`. If `A=0` when `x=1` and `A=2` when `x=-1`, then express `A` in terms of `x`.

Question No: #16

`y` is equal to the sum of two variables, one varies directly as `x` and other varies inversely as `x`. If `x=1, y=-1` and `x=3, y=5`, then find the relationship between `x` and `y`.
Ans: `y = 2x - 3/x`
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Question No: #17

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: #18

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: #19

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.