    Question

# In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

A
1
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B
102
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C
38
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D
42
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Solution

## The correct option is C 38Let A,B and C be the set of students opted for Mathematics, Physics and Chemistry respectively then, A={2,4,6,⋯,140} n(A)=70 B={3,6,9,⋯,138} n(B)=46 C={5,10,15,⋯,140} n(C)=28 (A∩B)={6,12,18,⋯,138} n(A∩B)=23 (A∩C)={10,20,30,⋯,140} n(A∩C)=14 (C∩B)={15,30,45,⋯,135} n(A∩B)=9 (A∩B∩C)={30,60,90,120} n(A∩C)=4 So, n(A∪B∪C)′= Total students − n(A∪B∪C) n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(A∩C)+n(A∩B∩C) =70+46+28−23−9−14+4=102 n(A∪B∪C)′=140−102=38  Suggest Corrections  108    Join BYJU'S Learning Program
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