JEE Main 2026 — Continuity and Differentiability Question with Solution
JEE Main 2026 (28 January Shift 2)
Question
Let . Consider the following two statements :
(I) is discontinous at .
(II) is continous at .
Then,
(I) is discontinous at .
(II) is continous at .
Then,
Choose an option
Show full solutionCorrect option: B
Correct answer
BNeither (I) nor (II) is True
Step-by-step explanation
Taking the limit as , we note for and for . This gives:
Continuity at :
,
is continuous at . So Statement (I) is false.
Continuity at :
Since LHL RHL, is discontinuous at . So Statement (II) is also false.
Hence, neither (I) nor (II) is true.
Continuity at :
,
is continuous at . So Statement (I) is false.
Continuity at :
Since LHL RHL, is discontinuous at . So Statement (II) is also false.
Hence, neither (I) nor (II) is true.
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Continuity and Differentiability chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2026, covering the Continuity and Differentiability 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.