Let $E = x^{2017} + y^{2017} + z^{2017} - 2017xyz$ (where $x, y, z \geq 0$),then the least value of $E$ is

If the geometric mean between $a$ and $b$ is $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$,then what is the value of $n$?

Let $0 < z < y < x$ be three real numbers such that $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in an arithmetic progression and $x, \sqrt{2}y, z$ are in a geometric progression. If $xy + yz + zx = \frac{3}{\sqrt{2}} xyz$,then $3(x + y + z)^2$ is equal to $............$.

The $A.M., H.M.$ and $G.M.$ between two numbers are $\frac{144}{15}$,$15$ and $12$,but not necessarily in this order. Then $H.M., G.M.$ and $A.M.$ respectively are

If $a^{1/x} = b^{1/y} = c^{1/z}$ and $a, b, c$ are in geometric progression,then $x, y, z$ are in.....

If $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $H.P.$,then