$a,\,g,\,h$ are arithmetic mean, geometric mean and harmonic mean between two positive numbers $x$ and $y$ respectively. Then identify the correct statement among the following
$h$ is the harmonic mean between $a$ and $g$
No such relation exists between $a, g$ and $h$
$g $ is the geometric mean between $a$ and $h$
$A$ is the arithmetic mean between $g$ and $h$
The geometric and harmonic means of two numbers $x_1$ and $x_2$ are $18$ and $16\frac {8}{13}$ respectively. The value of $|x_1 -x_2|$ is
If ${a_1},{a_2},....{a_n}$ are positive real numbers whose product is a fixed number $c$, then the minimum value of ${a_1} + {a_2} + ...$ $ + {a_{n - 1}} + 2{a_n}$ is
If $p,q,r$ are in $G.P$ and ${\tan ^{ - 1}}p$, ${\tan ^{ - 1}}q,{\tan ^{ - 1}}r$ are in $A.P.$ then $p, q, r$ are satisfies the relation
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
Let $m$ be the minimum possible value of $\log _3\left(3^{y_1}+3^{y_2}+3^{y_3}\right)$, where $y _1, y _2, y _3$ are real numbers for which $y _1+ y _2+ y _3=9$. Let $M$ be the maximum possible value of $\left(\log _3 x _1+\log _3 x _2+\log _3 x _3\right)$, where $x_1, x_2, x_3$ are positive real numbers for which $x_1+x_2+x_3=9$. Then the value of $\log _2\left(m^3\right)+\log _3\left(M^2\right)$ is. . . . . .