IPMAT Indore 2019 (MCQ) PYQs

Let ABC be an equilateral triangle, with each side of length $k$. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is

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

Let $\triangle ABC$ be a triangle right-angled at $B$ with $AB = BC = 18$. The area of the largest rectangle that can be inscribed in this triangle and has $B$ as one of the vertices is: