JEE Main 2026 — Application of Derivatives Question with Solution
JEE Main 2026 (24 January Shift 2)
Question
Consider the following three statements for the function defined by :
(I) is differentiable at all .
(II) is increasing in .
(III) is decreasing in .
Then.
(I) is differentiable at all .
(II) is increasing in .
(III) is decreasing in .
Then.
Choose an option
Show full solutionCorrect option: D
Correct answer
DOnly (I) and (III) are TRUE.
Step-by-step explanation
For : , (decreasing).
For : , (decreasing).
At : LHD , RHD . So is differentiable at .
(I) TRUE: is differentiable for all .
(II) FALSE: is decreasing in .
(III) TRUE: is decreasing in .
Only (I) and (III) are TRUE.
For : , (decreasing).
At : LHD , RHD . So is differentiable at .
(I) TRUE: is differentiable for all .
(II) FALSE: is decreasing in .
(III) TRUE: is decreasing in .
Only (I) and (III) are TRUE.
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This is a previous-year question from JEE Main 2026, covering the Application of Derivatives 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.