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Question

# In a survey of 200 students of a higher secondary school, it was found that 120 studied mathematics; 90 studied physics and 70 studied chemistry; 40 studied mathematics and physics; 30 studied physics and chemistry; 50 studied chemistry and mathematics, and 20 studied none of these subjects. If M, P and C represent the set of students who studied mathematics, physics and chemistry respectively, then

A
n(MPC)=180
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B
n(MPC)=20
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C
n(MPC)=40
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D
n(MPC)=20
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Solution

## The correct options are A n(M∪P∪C)=180 B n(M′∩P′∩C′)=20 D n(M∩P∩C)=20 Let U be the universal set. n(U)=200, n(M)=120, n(P)=90, n(C)=70, n(M∩P)=40, n(P∩C)=30, n(C∩M)=50, n(M′∩P′∩C′)=n(M∪P∪C)′=20 Now, n(M∪P∪C)′=n(U)−n(M∪P∪C) ⇒n(M∪P∪C)=180 n(M∪P∪C)=n(M)+n(P)+n(C) −n(M∩P)−n(P∩C)−n(C∩M) +n(M∩P∩C) ⇒n(M∪P∪C)=120+90+70−40−30−50+n(M∩P∩C) ⇒n(M∩P∩C)=180−160=20

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