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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Sets and Relations

JEE Main · Mathematics · Sets and Relations

A class has 175 students. The following data shows the number of...

A class has 175 students. The following data shows the number of students opting for 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. How& many students have offered Mathematics alone?

Options

  1. A35
  2. B48
  3. C60
  4. D22

Correct answer

C. 60

Step-by-step solution

Given, n(M)=100,n(P)=70,n(C)=40n\left(M\right) = 100, n\left(P\right) = 70, n\left(C\right) = 40

n(M∩P)=30,n(M∩C)=28,n\left(M \cap P\right) = 30, n\left(M \cap C\right) = 28,

n(P∩C)=23n\left(P \cap C\right) = 23 and n(M∩P∩C)=18n\left(M \cap P \cap C\right) = 18

∴n(M∩P′∩C′)=n[M∩(P∪C)′]∴ n\left(M \cap P^{′} \cap C^{′}\right) = n [ M \cap ( P \cup C)^{'} ]

=n(M)−[n(M∩P)+n(M∩C)−n(M∩P∩C)]= n\left(M\right) - [ n\left(M \cap P\right) + n\left(M \cap C\right) - n ( M \cap P \cap C ) ]

=100−[30+28−18]=60= 100 - [ 30 + 28 - 18 ] = 60
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