CAT (QA) PYQs

Suppose the medians $BD$ and $CE$ of a triangle $ABC$ intersect at a point $O$. If area of triangle $ABC$ is $108$ sq. cm., then, the area of the triangle $EOD$, in sq. cm., is

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of 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