Three positive numbers $a, b,$ and $c$ are in an Arithmetic Progression $(AP)$ and $abc = 4$. The minimum possible value of $b$ is:

Let $9 < x_1 < x_2 < \ldots < x_7$ be in an $A.P.$ with common difference $d$. If the standard deviation of $x_1, x_2, \ldots, x_7$ is $4$ and the mean is $\overline{x}$,then $\overline{x} + x_6$ is equal to:

The $8^{th}$ term of the series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ will be: (in $\sqrt{2}$)

Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^3y^4z^5 = (0.1)(600)^3$. Then $x^3 + y^3 + z^3$ is equal to

If twice the $11^{th}$ term of an Arithmetic Progression is equal to seven times its $21^{st}$ term,then its $25^{th}$ term is .......

If the $p^{th}$ term of an $A.P.$ is $\frac{1}{q}$ and the $q^{th}$ term is $\frac{1}{p}$,then the sum of its $pq$ terms is: