The interior angle of a $'n$' sided convex polygon are in $G.P$.. The smallest angle is $1^o $ and common ratio is $2^o $ then number of possible values of $'n'$ 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 $x,\;y,\;z$ are in $G.P.$ and ${a^x} = {b^y} = {c^z}$, then

If the range of $f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta}, \theta \in \mathbb{R}$ is $[\alpha, \beta]$, then the sum of the infinite $G.P.$, whose first term is $64$ and the common ratio is $\frac{\alpha}{\beta}$, is equal to...........

The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$, will be

$\alpha ,\;\beta $ are the roots of the equation ${x^2} - 3x + a = 0$ and $\gamma ,\;\delta $ are the roots of the equation ${x^2} - 12x + b = 0$. If $\alpha ,\;\beta ,\;\gamma ,\;\delta $ form an increasing $G.P.$, then $(a,\;b) = $