If the geometric mean of two positive numbers is $6$ and their arithmetic mean is $6.5$,then the numbers are.........

If the ratio of two numbers is $9:1$,then the ratio of their geometric mean to their harmonic mean is

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:

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 $............$.

Three non-zero real numbers form an $A.P.$ and the squares of these numbers taken in the same order form a $G.P.$ Then the number of all possible common ratios of the $G.P.$ is

If $a, b, c$ are in $A.P.$ as well as in $G.P.$,then