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

If the $n$ terms $a_1, a_2, \ldots, a_n$ are in $A$.$P$. with common difference $r$,then the difference between the mean of their squares and the square of their mean is

If three positive real numbers $a, b, c$ are in $A$.$P$. and $abc = 4$,then the minimum possible value of $b$ 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

Given the sum of the first $n$ terms of an $A.P.$ is $S_n = 2n + 3n^2$. Another $A.P.$ is formed with the same first term and double the common difference. The sum of $n$ terms of the new $A.P.$ is:

If the $7^{th}$ term of an Arithmetic Progression $(AP)$ is $40$,then the sum of its first $13$ terms is........