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
$15,\;12,\;\frac{{144}}{{15}}$
$\frac{{144}}{{15}},\;12,\;15$
$12,\;15,\;\frac{{144}}{{15}}$
$\frac{{144}}{{15}},\;15,\;12$
${2^{\sin \theta }} + {2^{\cos \theta }}$ is greater than
If ${\log _x}y,\;{\log _z}x,\;{\log _y}z$ are in $G.P.$ $xyz = 64$ and ${x^3},\;{y^3},\;{z^3}$ are in $A.P.$, then
If $a,\,b,\,c,\,d$ are positive real numbers such that $a + b + c + d$ $ = 2,$ then $M = (a + b)(c + d)$ satisfies the relation
If $a,\,b,\;c$ are in $A.P.$ and ${a^2},\;{b^2},\;{c^2}$ are in $H.P.$, then
If $x, y, z \in R^+$ such that $x + y + z = 4$, then maximum possible value of $xyz^2$ is -