IIM-K (BMSAT) 2025 (QA) PYQs

The perimeter of a rhombus is $148 \text{ cm}$ and one of its diagonals is $70 \text{ cm}$. Its area is equal to the area of a trapezium whose parallel sides are $x \text{ cm}$ and $50 \text{ cm}$ and the distance between the parallel sides is $14 \text{ cm}$. What is the value of $x$?

PQRS is a cyclic quadrilateral whose diagonals PR and QS intersect at the point T. $\angle SQR$ measures $72^\circ$, and $\angle QPR$ measures $28^\circ$. What is the measure of $\angle QRS$?

Points $P$, $Q$, $R$, and $S$ are taken on sides $AB$, $BC$, $CD$, and $DA$ of square $ABCD$ respectively, so that $\frac{AP}{PB} = \frac{BQ}{QC} = \frac{CR}{RD} = \frac{DS}{SA} = \frac{1}{n}$. Then the ratio of the area of $PQRS$ to the area of $ABCD$ is