IPMAT Indore (MCQ) 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

Let $\triangle ABC$ be a triangle with $AB = AC$ and $D$ be a point on $BC$ such that $\angle BAD = 30^\circ$. If $E$ is a point on $AC$ such that $AD = AE$, then $\angle CDE$ equals