IPMAT Indore 2024 (SA) PYQs

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

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

The number of triangles with integer sides and with perimeter 15 is: