CAT (QA) PYQs

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?

Students in a college have to choose at least two subjects from Chemistry, Mathematics and Physics. The number of students choosing all three subjects is $18$, choosing Mathematics as one of their subjects is $23$ and choosing Physics as one of their subjects is $25$. The smallest possible number of students who could choose Chemistry as one of their subjects is

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