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Question

# In a class of 55 students, the number of students studying different subjects are 23 in Mathematics and 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects, The number of students who have taken exactly one subject is

A
20
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B
24
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C
23
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D
22
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Solution

## The correct option is D 22Total no. of student=55Let n(M)=student who studying mathematicsn(C)=student who studying chemistryn(P)=student who studying Physics∴n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(M∩C)=9,n(P∩C)=7,n(M∩P∩C)=4Number of student who studying mathematics but not physic and chemistry⇒n(M)−[(n(M∩C)+n(M∩P)]+n(M∩P∩C)⇒23−[9+12]+4⇒23−21+4=6Number of student who studying chemistry but not physic and matehematics⇒n(C)−[(n(M∩C)+n(P∩C)]+n(M∩P∩C)⇒19−[9+7]+4⇒19−16+4=7Number of student who studying physics but not mathematics and chemistry⇒n(P)−[(n(M∩P)+n(P∩C)]+n(M∩P∩C)⇒24−[12+7]+4⇒24−19+4=9∴no. of student studying exactly one subject=6+7+9=22

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