CAT (QA) PYQs

In a group of $250$ students, the percentage of girls was at least $44\%$ and at most $60\%$. The rest of the students were boys. Each student opted for either swimming or running or both. If $50\%$ of the boys and $80\%$ of the girls opted for swimming while $70\%$ of the boys and $60\%$ of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

If $A=\left\{6^{2 n}-35 n-1: n=1,2,3, \ldots\right\}$ and $B=\{35(n-1): n=1,2,3, \ldots\}$ then which of the following is true?

For two sets $A$ and $B$, let $A \Delta B$ denote the set of elements which belong to $A$ or $B$ but not both. If $P=\{1,2,3,4\}, Q=\{2,3,5,6\},, R=\{1,3,7,8,9\}, S=$ $\{2,4,9,10\}$, then the number of elements in $(P \Delta Q) \Delta(R \Delta S)$ is