If $f(x + y,x - y) = xy\,,$ then the arithmetic mean of $f(x,y)$ and $f(y,x)$ is

Let $S_n$ and  $s_n$ deontes the sum of first $n$ terms of two different $A.P$. for which $\frac{{{s_n}}}{{{S_n}}} = \frac{{3n - 13}}{{7n + 13}}$ then  $\frac{{{s_n}}}{{{S_{2n}}}}$

If the sides of a right angled traingle are in $A.P.$, then the sides are proportional to

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

Let ${T_r}$ be the ${r^{th}}$ term of an $A.P.$ for $r = 1,\;2,\;3,....$. If for some positive integers $m,\;n$ we have ${T_m} = \frac{1}{n}$ and ${T_n} = \frac{1}{m}$, then ${T_{mn}}$ equals

If the sum of the $10$ terms of an $A.P.$ is $4$ times to the sum of its $5$ terms, then the ratio of first term and common difference is