CAT (QA) PYQs

Let $ABCD$ be a parallelogram. The lengths of the side $AD$ and the diagonal $AC$ a $10$ cm and $20$ cm, respectively. If the angle $\angle ADC$ is equal to $30^\circ$ then the area of the parallelogram, in sq. cm, is

If a rhombus has area $12 \mathrm{sq} \mathrm{cm}$ and side length $5 \mathrm{~cm}$, then the length, in cm, of its longer diagonal is

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