JEE Mains · Maths · STD 11 - 1. set theory
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 \(102\)
- B \(42\)
- C \(1\)
- D \(38\)
Answer & Solution
Correct Answer
(D) \(38\)
Step-by-step Solution
Detailed explanation
\(n(p)\, = \,\left[ {\frac{{140}}{3}} \right]\, = \,46\) \(n(C)\, = \,\left[ {\frac{{140}}{5}} \right]\, = \,28\) \(n(M)\, = \,\left[ {\frac{{140}}{2}} \right]\, = \,70\) \(n(p\, \cup \,C\, \cup \,M)\, = \,n(P)\, + \,n(C)\, + \,n(M)\) \( - \,n(P \cap C) - \,n(C \cap M) - \)…
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