CAT (QA) PYQs

The sides $A B$ and $C D$ of a trapezium $A B C D$ are parallel, with $A B$ being the smaller side. $P$ is the midpoint of $CD$ and $ABPD$ is a parallelogram. If the difference between the areas of the parallelogram $ABPD$ and the triangle $BPC$ is $10$ sq cm, then the area, in sq cm, of the trapezium $A B C D$ is

If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is