If all interior angles of a quadrilateral are in an $A.P.$ and the common difference is $10^{\circ}$,find the smallest angle. (in $^{\circ}$)

If $a^2 + b^2 + 16c^2 = 2(3ab + 6bc + 4ac)$,where $a, b, c$ are non-zero numbers,then $a, b, c$ are in:

Three numbers are selected from the set ${3^1, 3^2, 3^3, \dots, 3^{20}}$. Find the number of ways these selected numbers can form an increasing Geometric Progression $(G.P.)$.

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.

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