Three numbers are in $A.P.$ whose sum is $33$ and product is $792$. The smallest number among these is:

Sum of the series $1 \cdot 2015 + 2 \cdot 2014 + 3 \cdot 2013 + \dots + 2015 \cdot 1$ is equal to :-

The $n^{th}$ term of the series $\frac{2}{1!} + \frac{7}{2!} + \frac{15}{3!} + \frac{26}{4!} + \dots$ is

The sum of the first $n$ natural numbers is:

The minimum value of ${\left( {\frac{3}{a} - 1} \right)^2} + {\left( {\frac{a}{b} - 1} \right)^2} + {\left( {\frac{b}{c} - 1} \right)^2} + {\left( {3c - 1} \right)^2}$ where $0 < a, b, c \leqslant 9$,is $p - q\sqrt{r}$; $p, q, r \in I$ and $q, r$ are coprime,then $(p + q + r)$ is equal to

Let $S_1, S_2, \dots, S_{101}$ be the consecutive terms of an $A.P.$ If $\frac{1}{S_1 S_2} + \frac{1}{S_2 S_3} + \dots + \frac{1}{S_{100} S_{101}} = \frac{1}{6}$ and $S_1 + S_{101} = 50$, then $|S_1 - S_{101}|$ is equal to