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?

In a class of 150 students, 75 students chose physics, 111 students chose mathematics and 40 students chose chemistry. All students chose at least one of the three subjects and at least one student chose all three subjects. The number of students who chose both physics and chemistry is equal to the number of students who chose both chemistry and mathematics, and this is half the number of students who chose both physics and mathematics. The maximum possible number of students who chose physics but not mathematics, 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