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

If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and the product of the remaining two middle terms is $15$,then the greatest number of the series will be:

If the sum of $n$ terms of an $A.P.$ is $(pn + qn^2),$ where $p$ and $q$ are constants,find the common difference.

If $\frac{S_n}{S_m} = \frac{n^4}{m^4}$ (where $S_k$ is the sum of the first $k$ terms of an $A$.$P$. $a_1, a_2, \dots$),then the value of $\frac{a_{m+1}}{a_{n+1}}$ in terms of $m$ and $n$ is:

Let the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}$ be $\frac{5}{16}$, where $a > 2$. If $\alpha$ is such that $a, 4, \alpha, b$ are in $A$.$P$.,then the equation $\alpha x^2 - ax + 2(\alpha - 2b) = 0$ has :

If $2x, x + 8$ and $3x + 1$ are in an arithmetic progression,then $x = \dots$