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Variation
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Variation
All Questions (Page: 1)
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All Questions (PDF)
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Study Material (PDF)
All Questions (PDF)
Self Assesment
Sort As
Serial Number
Newly Added
Language
English
Bengali
Click on each question to see answer & solution.
Question No: #1
If `(a+b) \propto \sqrt{ab}`, then show that `(\sqrt{a}+\sqrt{b}) \propto (\sqrt{a}-\sqrt{b})`.
Ans:
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Question No: #2
If `a \propto b` and `b \propto c`, then prove that `a^3+b^3+c^3 \propto abc`.
Ans:
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Question No: #3
`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: #4
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.
Ans:
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Question No: #5
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: #6
If `x \propto y` and `y \propto z`, then prove that `x^2+y^2+z^2 \propto xy+yz+zx`.
Ans:
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Question No: #7
If `(x^3 - 1/y^3) \propto (x^3 + 1/y^3)`, then prove that `x \propto 1/y`.
Ans:
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Question No: #8
If `(a+b) \propto (a-b)`, then prove that `a^2+b^2 \propto ab`.
Ans:
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Question No: #9
If `(a^2+b^2) \propto ab`, then prove that, `(a+b) \propto (a-b)`.
Ans:
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Question No: #10
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`.
Ans:
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