If for an Arithmetic Progression $(AP)$,$9$ times the $9^{th}$ term is equal to $13$ times the $13^{th}$ term,then the value of the $22^{nd}$ term is:

Given that $n$ $A$.$M$.'s are inserted between two sets of numbers $a, 2b$ and $2a, b$,where $a, b \in R$. Suppose further that the $m^{th}$ mean between these sets of numbers is the same,then the ratio $a:b$ equals

Find the sum of odd integers from $1$ to $2001$.

If $a, b,$ and $c$ are positive real numbers,then the minimum value of $(a + b + c)(1/a + 1/b + 1/c)$ is .......

The sum of all two-digit numbers which,when divided by $4$,yield unity as a remainder is:

If $a_1, a_2, a_3, ......., a_n$ are in $A.P.$,where $a_i > 0$ for all $i$,then the value of $\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + ....... + \frac{1}{\sqrt{a_{n-1}} + \sqrt{a_n}} = $