If $p,\;q,\;r$ are in one geometric progression and $a,\;b,\;c$ in another geometric progression, then $cp,\;bq,\;ar$ are in

Let $\alpha$ and $\beta$ be the roots of the equation $\mathrm{px}^2+\mathrm{qx}-$ $r=0$, where $p \neq 0$. If $p, q$ and $r$ be the consecutive terms of a non-constant G.P and $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}$, then the value of $(\alpha-\beta)^2$ is :

The sum of an infinite geometric series with positive terms is $3$ and the sum of the cubes of its terms is $\frac {27}{19}$. Then the common ratio of this series is

If $\frac{{a + bx}}{{a - bx}} = \frac{{b + cx}}{{b - cx}} = \frac{{c + dx}}{{c - dx}},\left( {x \ne 0} \right)$ then $a$, $b$, $c$, $d$ are in

If $a,\;b,\;c$ are in $A.P.$, $b,\;c,\;d$ are in $G.P.$ and $c,\;d,\;e$ are in $H.P.$, then $a,\;c,\;e$ are in

If the first term of a $G.P. a_1, a_2, a_3......$ is unity such that $4a_2 + 5a_3$ is least, then the common ratio of $G.P.$ is