Let $E = x^{2017} + y^{2017} + z^{2017} - 2017xyz$ (where $x, y, z \geq 0$),then the least value of $E$ is

The $6^{th}$ term of a $G.P.$ is $32$ and its $8^{th}$ term is $128$,then the common ratio of the $G.P.$ is

The first and last terms of an $AP$ are $75$ and $375$ respectively. If its sum is $3600$,find the number of terms in the $AP$ and its common difference.

If $a, b, c$ are in $H.P.$,then the value of $\left( {\frac{1}{b} + \frac{1}{c} - \frac{1}{a}} \right)\left( {\frac{1}{c} + \frac{1}{a} - \frac{1}{b}} \right)$ is

Let $a_n$ be a sequence such that $a_1 = 5$ and $a_{n+1} = a_n + (n - 2)$ for all $n \in N$. Then $a_{51}$ is:

If the sum of the series $54 + 51 + 48 + \dots$ is $513$, then the number of terms is: