CAT (QA) PYQs

Let $A B C$ be a right-angled triangle with $B C$ as the hypotenuse. Lengths of $A B$ and AC are $15 \mathrm{~km}$ and $20 \mathrm{krn}$, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of $30 \mathrm{~km}$ per hour is

The length of each side of an equilateral triangle ABC is $3 \mathrm{~cm}$. Let D be a point on BC such that the area of triangle ADC is half the area of triangle $A B D$. Then the length of $A D$, in 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