IPMAT Indore (MCQ) PYQs

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

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 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