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

In a triangle ABC, let D be the midpoint of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be

The side AB of a triangle ABC is c. The median BD is of length k. If $\angle BDA = \theta$ and $\theta < 90^\circ$, then the area of triangle ABC is