If $a,\;b,\;c$ are in $A.P.$ and $a,\;c - b,\;b - a$ are in $G.P. $ $(a \ne b \ne c)$, then $a:b:c$ is

If the equation $x^8 - kx^2 + 3 = 0$ has a real solution, then least integral value of $k$ is-

If $a, b, c$ are in $A.P.;$ $b, c, d$ are in $G.P.$ and $\frac{1}{c}, \frac{1}{d}, \frac{1}{e}$ are in $A.P.$ prove that $a, c, e$ are in $G.P.$

If three unequal non-zero real numbers $a,\;b,\;c$ are in $G.P.$ and $b - c,\;c - a,\;a - b$ are in $H.P.$, then the value of $a + b + c$ is independent of

If $m$ is the $A.M$ of two distinct real numbers $ l$  and $n (l,n>1) $ and  $G_1, G_2$ and $G_3$ are three geometric means between  $l$ and $n$ then $G_1^4 + 2G_2^4 + G_3^4$ equals :

Let $x, y>0$. If $x^{3} y^{2}=2^{15}$, then the least value of $3 x +2 y$ is