Question

In a class of $175$ students, the following data shows the number of students opting one or more subjects.
Mathematics $100$; Physics $70$; Chemistry $40$; Mathematics and Physics $30$; Mathematics and Chemistry $28$; Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$.
Then, number of students opted Mathematics alone is

• A. 35
• B. 48
• C. 60
• D. 20

Answer 1

Answer: (C)

Given, $n(M)=100, n(P)=70, n(C)=40$
$n(M \cap P)=30, n(M \cap C)=28 $
$ n(P \cap C)=23$
and $ n(M \cap P \cap C)=18$
$ \therefore n\left(M \cap P^{\prime} \cap C^{\prime}\right)=n\left[M \cap(P \cup C)^\gamma\right] $
$ =n(M)-n[M \cap(P \cup C)] $
${\left[\because n\left(A \cap B^{\prime}\right)=n(A)-n(B)\right]}$
$=n(M)-n[(M \cap P) \cup(M \cap C)] $
$=n(M)-[n(M \cap P)+n(M \cap C)$
$ -n(M \cap P \cap C)] $
$=100-[30+28-18]$
$ =100-40 $
$ =60$