Variation

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

Click on each question to see answer & solution.

Question No: #21

If `x/y \propto (x+y)` and `y/x \propto (x-y)` then prove that `(x^2-y^2)` is constant.

Question No: #22

If `y \propto x^2` and `y=9` when `x=9`. Then find the value of `x` when `y=4`
Ans: `\pm 6`
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Question No: #23

The square of `y` is directly proportional to `x`. `y=2a` when `x=a`, then find the relationship between `x` and `y`.
Ans: `y^2=4ax`
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Question No: #24

The cube of `y` is inversely proportional to the square of `x` and `y=3` when `x=16`; Find the value of `y` if `x=2`.

Question No: #25

If `x \propto yz` and `y \propto zx`, then show that `z` is a non-zero constant.

Question No: #26

If `a, b, c, d` are constants and `ax + b/y \propto cx+d/y`, then prove that, `xy` is constant.

Question No: #27

If `2x+3y \propto 3x-4y`, then show that, `x^3-y^3 \propto xy(x+y)`.

Question No: #28

If `(a+b) \propto (a-b)`, then prove that - (i) `a^2+b^2 \propto ab`, (ii) `a^3+b^3 \propto a^3-b^3`

Question No: #29

If `x^3 + y^3 \propto x^3-y^3`, then show that, `x+y \propto x-y`

Question No: #30

If `(a^2+b^2) \propto ab`, then prove that, `(a+b) \propto (a-b)`.