The product of three consecutive terms of a $G.P.$ is $512$. If $4$ is added to each of the first and the second of these terms, the three terms now form an $A.P.$ Then the sum of the original three terms of the given $G.P.$ is
$36$
$32$
$24$
$28$
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
If $p, q, r$ are in $G.P.$ and the equations, $p x^{2}+2 q x+r=0$ and $d x^{2}+2 e x+f=0$ have a common root, then show that $\frac{d}{p}, \frac{e}{q}, \frac{f}{r}$ are in $A.P.$
If the equation $x^8 - kx^2 + 3 = 0$ has a real solution, then least integral value of $k$ is-
The product of $n$ positive numbers is unity. Their sum is
If the arithmetic, geometric and harmonic means between two positive real numbers be $A,\;G$ and $H$, then