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Variation
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Variation
All Questions (Page: 6)
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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: #51
If `x \propto 1/y`, then show that `x+y` will be minimum when `x=y`.
Ans:
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Question No: #52
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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Question No: #53
`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: #54
`y` is equal to the sum of two variables, one varies directly as `x` and other varies directly as `x^2`. If `x=1` when `y=3` and `x=2` when `y=10`, then find the relationship between `x` and `y`.
Ans: `y=x+2x^2`
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Question No: #55
If `x \propto (y+z)`, `y \propto (z+x)` and `z \propto (x+y)`, and the variation constants are `l, m, n`, then prove that, `\frac{l}{l+1} + \frac{m}{m+1} + \frac{n}{n+1} = 1`
Ans:
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Question No: #56
If `x+z \propto y` and `y+z \propto x`, then show that, `x+y \propto z`.
Ans:
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Question No: #57
If `(x+y) \propto z` when `y` is constant and `(z+x) \propto y` when `z` is constant. Then prove that `(x+y+z) \propto yz`, when `y` and `z` are both vary.
Ans:
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Question No: #58
If `x, y, z` are variables, but `(y+z-x)` is constant and if `(x+y-z)(x-y+z) \propto yz`, then prove that, `(x+y+z) \propto yz`.
Ans:
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Question No: #59
`x, y, z` are three variables such that `x+y+z =` constant and `(x-y+z)(x+y-z) \propto yz`, then prove that, `(y+z-x) \propto yz`.
Ans:
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Question No: #60
If `a, b, h, l, m` are all constants and if `ax^2+2hxy+by^2 \propto z^2` and `lx+my \propto z`, then show that, `x \propto y` ред
Ans:
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