If $a, b, c$ are in $G.P.$ and $a + x, b + x, c + x$ are in $H.P.$,then the value of $x$ is ($a, b, c$ are distinct numbers).

The product of $n$ positive numbers is $1$. The sum of these numbers cannot be less than what value?

If the ratio of the harmonic mean to the geometric mean of two positive numbers $a$ and $b$ $(a > b)$ is $4 : 5$,then $a : b = \dots$ (in $: 1$)

In a set of four numbers,the first three are in $G.P.$ and the last three are in $A.P.$ with a common difference of $6$. If the first and last numbers are equal,then the first number is:

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of an Arithmetic Progression are equal to the terms of a Geometric Progression,and these terms are $x, y, z$ respectively,then $x^{y - z} \cdot y^{z - x} \cdot z^{x - y} = \dots$

If $a, b, c$ are in $A.P.$ and $a, b, d$ are in $G.P.$,then $a, a - b, d - c$ will be in