Find the $10^{th}$ term of the geometric series $5+25+125+\ldots$

If $\omega$ is a non-real root of the equation $x^3 - 1 = 0$,then the value of $\sum_{r=1}^5 (1 + \omega^r + \omega^{2r})$ is

If $\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \dots + \infty = \frac{\pi^4}{90}$,then the value of $\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \dots + \infty$ is

The number $111...1$ ($91$ times) is a:

If $4^{th}$ and $8^{th}$ terms of a $G.P.$ are $24$ and $384$ respectively,then find out the first term and common ratio.

The $G.M.$ of the roots of the equation $x^2 - 18x + 9 = 0$ is