IPMAT Indore (MCQ) PYQs

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

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 acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is