IPMAT Indore (SA) PYQs

The number of pairs $(x, y)$ of integers satisfying the inequality $|x - 5| + |y - 5| \leq 6$ is:

If $n$ is an integer such that $\frac{|n+6|-|n-3|}{\sqrt{100-n^3}} \geq 0$, then the number of possible values of $n$ is ___

The length of the line segment joining the two intersection points of the curves $y = 4970 - |x|$ and $y = x ^ 2$ is