CAT (QA) PYQs

In a triangle $ABC$ , medians $AD$ and $BE$ are perpendicular to each other, and have lengths $12 \mathrm{~cm}$ and $9 \mathrm{~cm}$, respectively. Then, the area of triangle $ABC$, in sq cm, is

Let $T$ be the triangle formed by the straight line $3x + 5y - 45 = 0$ and the coordinate axes. Let the circumcircle of $T$ have radius of length $L,$ measured in the same unit as the coordinate axes. Then, the integer closest to $L$ is

In a $\triangle ABC$, points $D$ and $E$ are on the sides $BC$ and $AC$, respectively. $BE$ and $AD$ intersect at point $T$ such that $AD:AT = 4:3$, and $BE:BT = 5:4$. Point $F$ lies on $AC$ such that $DF$ is parallel to $BE$. Then, $BD:CD$ is