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

For any three positive real numbers $a, b, c$,if $9(25a^2 + b^2) + 25(c^2 - 3ac) = 15b(3a + c)$,then:

If $\sum_{i = 1}^n i = \frac{n(n + 1)}{2}$,then $\sum_{i = 1}^n (3i - 2) = $

Let $S_n = 1 + q + q^2 + ..... + q^n$ and $T_n = 1 + \left( \frac{q + 1}{2} \right) + \left( \frac{q + 1}{2} \right)^2 + ...... + \left( \frac{q + 1}{2} \right)^n$ where $q$ is a real number and $q \neq 1$. If $^{101}C_1 + ^{101}C_2 \cdot S_1 + ...... + ^{101}C_{101} \cdot S_{100} = \alpha \cdot T_{100}$,then $\alpha$ is equal to

If the sum of three terms of a $G.P.$ is $19$ and their product is $216$,then the common ratio of the series is

The sum of an infinite $G.P.$ with common ratio $r$ can be found if: