If S= R:|2 a-1|=3[a]+2, where [t] denotes the greatest integer less than or equal to t and represents the fractional part of t, then 72 Σ a S a is equal to _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2024 Mathematics question

JEE Main 2024 · 5 Apr, Morning shift · Q38

JEE Main 20245 Apr, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

S=\{a \in \mathbf{R}:|2 a-1|=3[a]+2\{a \}\}

, where

[t]

denotes the greatest integer less than or equal to

t

and

\{t\}

represents the fractional part of

t

, then

72 \sum_\limits{a \in S} a

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.