CAT (QA) PYQs

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

Let $\triangle ABC$ be an isosceles triangle such that $AB$ and $AC$ are of equal length. $AD$ is the altitude from $A$ on $BC$ and $BE$ is the altitude from $B$ on $AC$. If $AD$ and $BE$ intersect at $O$ such that $\angle AOB = 105^\circ$, then $AD/BE$ equals

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