IPMAT Indore (SA) PYQs

Let $A$ and $B$ be two sets such that the Cartesian product $A \times B$ consists of four elements. If two elements of $A \times B$ are $(1,4)$ and $(4,1)$, then

In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. Then at least ________ percentage of students passed both their Physics and Mathematics examinations.

Let A and B be two finite sets such that $n(A - B)$, $n(A\cap B)$, $n(B - A)$ are in an arithmetic progression. Here $n(X)$ denotes the number of elements in a finite set $X$. If $n(A\cup B) = 18$, then $n(A) + n(B)$ is ____