If $a^{1/x} = b^{1/y} = c^{1/z}$ and $a, b, c$ are in $G.P.$,then $x, y, z$ will be in

In a $G.P.$,the sum of three numbers is $14$. If $1$ is added to the first two numbers and subtracted from the third number,the series becomes an $A.P.$. Then,the greatest number is:

Suppose $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $G.P.$ If $a < b < c$ and $a + b + c = \frac{3}{2}$,then the value of $a$ is

If $a, b, c$ are in $A.P.$,then $10^{ax + 10}, 10^{bx + 10}, 10^{cx + 10}$ will be in

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

If the arithmetic,geometric,and harmonic means between two distinct positive real numbers are $A, G,$ and $H$ respectively,then the relation between them is