Variation

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

Click on each question to see answer & solution.

Question No: #41

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

Question No: #42

If `(1/x^3 + 1/y^3) \propto \frac{1}{x^3+y^3}`, then show that, `x \propto y` ред

Question No: #43

If `(u^2 + v^2) \propto (x^2+y^2)` and `uv \propto xy`, then show that, `(u+v) \propto (x+y)` when `u/v + v/u = x/y + y/x`.

Question No: #44

If `(ax+by) \propto \sqrt{xy}`, then show that, `(ax)^2+(by)^2 \propto xy` (where `a` and `b` are constants).

Question No: #45

If `ax - by \propto \sqrt{xy}`, then show that, `x^2 + y^2 \propto xy`

Question No: #46

If `2x^2+3y^2 \propto xy`, then prove that, `9x^4+4y^4 \propto x^2y^2`.

Question No: #47

If `b \propto a^3` and `a` increases 10%, then find what percent `b` will be increased?
Ans: 33.1%
SEE SOLUTION

Question No: #48

If `b \propto a^3` and `a` increases in the ratio of `2:3`, then find in what ratio `b` will be increased.
Ans: `8:27`
SEE SOLUTION

Question No: #49

If `x \propto 1/y^2`, then in what ratio `x` changes when `y` changes at a ratio of `9:5`?
Ans: `25:81`
SEE SOLUTION

Question No: #50

If `x \propto y/z^2` and `y` increases by 20% and `z` increases by 25%, then in what percentage will be `x` increased or decreased?
Ans: `23 1/5 %`
SEE SOLUTION