IPMAT Indore (MCQ) PYQs

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

In triangle $ABC, AB = AC = x, ∠ABC = \theta$ and the circumradius is equal to $y$. Then $\frac{x}{y}$ equals

Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the triangle in such a way that the shortest distance of the dog from the triangle is exactly 1 meter. The total distance covered (in meters) by the dog in one round is