IPMAT Indore (SA) 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 right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is

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