IPMAT Indore 2023 (MCQ) PYQs

Out of 80 students who appeared for the school exams in Mathematics (M), Physics (P) and Chemistry (C), 50 passed M, 30 passed P and 40 passed C. At most 20 students passed M and P, at most 20 students passed P and C, and at most 20 students passed C and M. The maximum number of students who could have passed all three exams is __________.

In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. The number of students who did not opt for any of the three sports is

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