The sum of $24$ terms of the following series $\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + .........$ is

If ${A_1},\,{A_2}$ be two arithmetic means between $\frac{1}{3}$ and $\frac{1}{{24}}$ , then their values are

Find the $7^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=\frac{n^{2}}{2^{n}}$

If the roots of the equation ${x^3} - 12{x^2} + 39x - 28 = 0$ are in $A.P.$, then their common difference will be

If the sum of the series $2 + 5 + 8 + 11............$ is $60100$, then the number of terms are

If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is