Let ${a_n}$ be the ${n^{th}}$ term of the G.P. of positive numbers. Let $\sum\limits_{n = 1}^{100} {{a_{2n}}} = \alpha $ and $\sum\limits_{n = 1}^{100} {{a_{2n - 1}}} = \beta $, such that $\alpha \ne \beta $,then the common ratio is
$\frac{\alpha }{\beta }$
$\frac{\beta }{\alpha }$
$\sqrt {\frac{\alpha }{\beta }} $
$\sqrt {\frac{\beta }{\alpha }} $
If $a, b$ and $c$ be three distinct numbers in $G.P.$ and $a + b + c = xb$ then $x$ can not be
If ${\log _a}x,\;{\log _b}x,\;{\log _c}x$ be in $H.P.$, then $a,\;b,\;c$ are in
Let $M=2^{30}-2^{15}+1$, and $M^2$ be expressed in base $2$.The number of $1$'s in this base $2$ representation of $M^2$ is
If $p,\;q,\;r$ are in one geometric progression and $a,\;b,\;c$ in another geometric progression, then $cp,\;bq,\;ar$ are in
If the $n^{th}$ term of geometric progression $5, - \frac{5}{2},\frac{5}{4}, - \frac{5}{8},...$ is $\frac{5}{{1024}}$, then the value of $n$ is