JEE Main 2021 — Definite Integration Question with Solution
From: JEE Main 2021 (Online) 20th July Morning Shift
Question
Let a be a positive real number such that where [ x ] is the greatest integer less than or equal to x. Then a is equal to:
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
a > 0
Let
a=\matrix{ {[a]} & + & {\{ a\} } \cr \Downarrow & {} & \Downarrow \cr {G.I.F.} & {} & {Fractional\,part} \cr }
Here [ a ] = n
Now,
n = 0 and {a} = loge 2
So,
Option (2) is correct.
Let
a=\matrix{ {[a]} & + & {\{ a\} } \cr \Downarrow & {} & \Downarrow \cr {G.I.F.} & {} & {Fractional\,part} \cr }
Here [ a ] = n
Now,
n = 0 and {a} = loge 2
So,
Option (2) is correct.
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This is a previous-year question from JEE Main 2021, covering the Definite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.