CAT (QA) PYQs

From a triangle $ABC$ with sides of lengths $40$ ft, $25$ ft and $35$ ft, a triangular portion $GBC$ is cut off where $G$ is the centroid of $ABC$. The area, in sq ft, of the remaining portion of triangle $ABC$ is

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio $a: b$. If the radius of the circle is $r$, then the area of the triangle is

Given an equilateral triangle $\mathrm{T} 1$ with side $24 \mathrm{~cm}$, a second triangle $\mathrm{T} 2$ is formed by joining the midpoints of the sides of $\mathrm{T} 1$. Then a third triangle $\mathrm{T} 3$ is formed by joining the midpoints of the sides of $\mathrm{T} 2$. If this process of forming triangles is continued, the sum of the areas, in sq cm , of infinitely many such triangles $\mathrm{T} 1, \mathrm{~T} 2, \mathrm{~T} 3, \ldots$ will be