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
102
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B
42
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C
1
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D
38
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Solution

The correct option is D 38Let n(A)= number of students opted Mathematics =70,n(B)= number of students opted Physics =46,n(C)= number of students opted Chemistry =28,n(A∩B)=23,n(B∩C)=9,n(A∩C)=14,n(A∩B∩C)=4,Now 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=102Si number of students not opted for any course = Total −n(A∩B∩C)=140−102=38.

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