Variation

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

Click on each question to see answer & solution.

Question No: #31

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

Question No: #32

If `x \propto y` and `y \propto z`, then prove that, `\sqrt{xy} \propto z`.

Question No: #33

If `x \propto y, y \propto z` then prove that, `(x+y+z) \propto (\sqrt{xy} + \sqrt{yz} + \sqrt{zx})`.

Question No: #34

If `x \propto y` and `y \propto z`, then prove that `x^2+y^2+z^2 \propto xy+yz+zx`.

Question No: #35

If `a \propto b` and `b \propto c`, then prove that `a^3+b^3+c^3 \propto abc`.

Question No: #36

If `a \propto b, b \propto c`, then prove that, `a^3b^3 + b^3c^3 + c^3a^3 \propto abc(a^3+b^3+c^3)`

Question No: #37

If `(x^3 - 1/y^3) \propto (x^3 + 1/y^3)`, then prove that `x \propto 1/y`.

Question No: #38

`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: #39

If `1/x + 1/y \propto \frac{1}{x+y}`, then show that the value of `x/y + y/x` is a constant.

Question No: #40

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