IPMAT Indore Number System > Integral Solutions PYQs

The number of integer solutions $(x, y)$ of the inequality $x^2 + y^2 \leq 10$ is

If $m$ and $n$ are two positive integers such that $7m + 11n = 200$, then the minimum possible value of $m + n$ is

Let $[x]$ denote the greatest integer not exceeding $x$ and {$x$} $= x - [x]$ If $n$ is a natural number, then the sum of all values of $x$ satisfying the equation $2[x] = x + n${$x$} is

If $|x| <100$ and $|y| <100$, then the number of integer solutions of $(x, y)$ satisfying the equation $4x + 7y = 3$ is