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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 option is D n(MPC)=20
Let U be the universal set.
n(U)=200,
n(M)=120, n(P)=90, n(C)=70,
n(MP)=40, n(PC)=30, n(CM)=50,
n(MPC)=n(MPC)=20

Now, n(MPC)=n(U)n(MPC)
n(MPC)=180
n(MPC)=n(M)+n(P)+n(C) n(MP)n(PC)n(CM) +n(MPC)
n(MPC)=120+90+70403050+n(MPC)
n(MPC)=180160=20

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