JEE 2023 — Mathematics PYQ

1. Formula ka upyog karte hain:

   $$n(A\cup B\cup C)=n(A)+n(B)+n(C)-[n(A\cap B)+n(B\cap C)+n(C\cap A)]+n(A\cap B\cap C)$$
   $$60=48+25+18-(\text{Sum of intersections})+5$$
   $$60=91+5-(\text{Sum of intersections})$$
   $$\text{Sum of intersections}=96-60=36$$

2. "Exactly two events" nikalne ka formula:

   $$\text{Exactly two}=[n(A\cap B)+n(B\cap C)+n(C\cap A)]-3\times n(A\cap B\cap C)$$
   $$\text{Exactly two}=36-3(5)$$
   $$\text{Exactly two}=36-15=21$$

Answer: (3) 21