JEE Mains · Maths · STD 11 - 1. set theory
If \(\mathrm{S}=\{\mathrm{a} \in \mathrm{R}:|2 \mathrm{a}-1|=3[\mathrm{a}]+2\{\mathrm{a}\}\}\), where \([\mathrm{t}]\) denotes the greatest integer less than or equal to \(t\) and \(\{t\}\) represents the fractional part of \(t\), then \(72 \sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}\) is equal to ....................
- A \(18\)
- B \(16\)
- C \(13\)
- D \(75\)
Answer & Solution
Correct Answer
(A) \(18\)
Step-by-step Solution
Detailed explanation
\( |2 \mathrm{a}-1|=3[\mathrm{a}]+2\{\mathrm{a}\} \) \( |2 \mathrm{a}-1|=[\mathrm{a}]+2 \mathrm{a}\) Case \(-1\) : \(\mathrm{a}>\frac{1}{2} \) \( 2 \mathrm{a}-1=[\mathrm{a}]+2 \mathrm{a} \) \( {[\mathrm{a}]=-1 \quad \therefore \mathrm{a} \in[-1,0) \text { Reject }} \)…
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