JEE Mains · Maths · STD 11 - 1. set theory
Let \(\mathrm{A}=\{\mathrm{n} \in[100,700] \cap \mathrm{N}: \mathrm{n}\) is neither a multiple of \(3\) nor a multiple of 4\(\}\). Then the number of elements in \(\mathrm{A}\) is
- A \(300\)
- B \(280\)
- C \(310\)
- D \(290\)
Answer & Solution
Correct Answer
(A) \(300\)
Step-by-step Solution
Detailed explanation
\( \mathrm{n}(3) \Rightarrow \text { multiple of } 3 \) \( 102,105,108, \ldots . ., 699 \) \( \mathrm{~T}_{\mathrm{n}}=699=102+(\mathrm{n}-1)(3) \) \( \mathrm{n}=200 \) \( \mathrm{n}(3)=200 \) \( \because \mathrm{n}(4) \Rightarrow\) multiple of \(4\)…
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