JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Sets and Relations

JEE Main · Mathematics · Sets and Relations

If in a class there are 200 students in which 120 take Mathematics,...

If in a class there are

200

students in which

120

take Mathematics,

90

take Physics,

60

take Chemistry,

50

take Mathematics & Physics,

50

take Mathematics & Chemistry,

43

take Physics & Chemistry and

38

take Mathematics, Physics & Chemistry, then the number of students who have taken exactly one subject is

Options

A $42$
B $56$
C $270$
D $98$

Correct answer

D. $98$

Step-by-step solution

Let,

M \to

Mathematics,

P \to

Physics,

C \to

Chemistry
Given that total students

= 200

n\left(M\right) = 120,n\left(P\right) = 90, n\left(C\right) = 60

n\left(M \cap P\right) = 50,n\left(M \cap C\right) = 50, n\left(P \cap C\right) = 43

n\left(M \cap P \cap C\right) = 38

Required number of students taking exactly one subject is

n\left(M\right) + n\left(P\right) + n \left(

C\right) - 2n \left(M \cap P\right) - 2n \left(

P \cap C\right) -

2n\left(

M \cap C\right) +

3n\left(

M \cap P \cap C\right)

= 120 + 90 + 60 - 2 \left(50\right) - 2 \left(

50\right) -

2\left(

43\right) +

3\left(

38\right)

<br/>

= 98

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