If the numbers $a, b, c, d, e$ form an $A.P.$,then the value of $a - 4b + 6c - 4d + e$ is

If $x, y, z \in R^+$ such that $x + y + z = 4$,then the maximum possible value of $xyz^2$ is -

If $a, b, c$ are in $A.P.$,then $\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$ will be in

If the sum of the first $n$ terms of an arithmetic progression is $cn^2$,what is the sum of the squares of these $n$ terms?

If the sum of the first $21$ terms of the series $\log _{9^{1 / 2}} x + \log _{9^{1 / 3}} x + \log _{9^{1 / 4}} x + \dots$ where $x > 0$ is $504$,then $x$ is equal to:

Which of the following sequences is an arithmetic sequence?