IPMAT Indore 2024 (SA) PYQs

The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices $(0, 0), (0, 31),$ and $(31, 0)$ is

The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

The lengths of the sides of a triangle are $x, 21$ and $40$, where $x$ is the shortest side. A possible value of $x$ is: