CAT (QA) PYQs

Points $E, F, G, H$ lie on the sides $A B, B C, C D$, and $D A$, respectively, of a square $A B C D$. If $E F G H$ is also a square whose area is $62.5 \%$ of that of $ABCD$ and $CG$ is longer than $EB$ , then the ratio of length of $EB$ to that of $CG$ is

In a parallelogram $ABCD$ of area $72 \mathrm{sq} \mathrm{cm}$, the sides $CD$ and $AD$ have lengths $9 \mathrm{~cm}$ and $16 \mathrm{~cm}$, respectively. Let P be a point on $C D$ such that $A P$ is perpendicular to $C D$. Then the area, in sq cm, of triangle $A P D$ is

A park is shaped like a rhombus and has area $96$ sq m. If $40$ m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of $125$ per m, is