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

For a series $S = 1 -2 + 3\, -\, 4 … n$ terms,

Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd. 

Statement $-2$ : Sum of series is $-\frac {n}{2}$ when value of $n$ is any even integer

Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ 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 ${m^{th}}$ mean between these sets of numbers is same, then the ratio $a:b$ equals

For $\mathrm{x} \geq 0$, the least value of $\mathrm{K}$, for which $4^{1+\mathrm{x}}+4^{1-\mathrm{x}}$, $\frac{\mathrm{K}}{2}, 16^{\mathrm{x}}+16^{-\mathrm{x}}$ are three consecutive terms of an $A.P.$ is equal to :

If all interior angle of quadrilateral are in $A.P.$ If common difference is $10^o$, then find smallest angle ? .............. $^o$