JEE Main 2012 — Continuity and Differentiability Question with Solution
JEE Main 2012 (19 May Online)
Question
Let be a function satisfying , for all and , where is the set of all real numbers and denotes the largest integer less than or equal to .
Statement 1: exists.
Statement 2: is continuous at .
Choose an option
Show full solutionCorrect option: D
Correct answer
DStatement 1 is true, Statement 2 is false.
Step-by-step explanation
[By Sandwich theorem]
Now
Hence by Sandwich theorem does not exists.
Therefore is not continuous at . Thus statement-1 is true but statement- 2 is not true
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This is a previous-year question from JEE Main 2012, 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.