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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

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

If in a class there are 200200 students in which 120120 take Mathematics, 9090 take Physics, 6060 take Chemistry, 5050 take Mathematics & Physics, 5050 take Mathematics & Chemistry, 4343 take Physics & Chemistry and 3838 take Mathematics, Physics & Chemistry, then the number of students who have taken exactly one subject is

Options

  1. A4242
  2. B5656
  3. C270270
  4. D9898

Correct answer

D. 9898

Step-by-step solution

Let, M→M \to Mathematics, P→P \to Physics, C→C \to Chemistry
Given that total students =200= 200
n(M)=120,n(P)=90,n(C)=60n\left(M\right) = 120, n\left(P\right) = 90, n\left(C\right) = 60
n(M∩P)=50,n(M∩C)=50,n(P∩C)=43n\left(M \cap P\right) = 50,n\left(M \cap C\right) = 50, n\left(P \cap C\right) = 43
n(M∩P∩C)=38n\left(M \cap P \cap C\right) = 38
Required number of students taking exactly one subject is
n(M)+n(P)+n(C)−2n(M∩P)−2n(P∩C)−2n(M∩C)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(M∩P∩C)3n \left(M \cap P \cap C\right)
=120+90+60−2(50)−2(50)−2(43)= 120 + 90 + 60 - 2 \left(50\right) - 2 \left(50\right) - 2\left(43\right)+ 3(38)3 \left(38\right)
=98= 98
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