JEE Main 2021MathematicsContinuity and DifferentiabilityMediumMCQ

JEE Main 2021 — Continuity and Differentiability Question with Solution

JEE Main 2021 (26 Aug Shift 2)

Question

Let [t] denote the greatest integer less than or equal to t.
Let f(x)=x-[x], g(x)=1-x+[x], and h(x)=min{f(x),g(x)},x∈[-2,2]. Then h is :

Choose an option

Show full solutionCorrect option: A
Correct answer
Acontinuous in [-2,2] but not differentiable at more than four points in (-2,2)

Step-by-step explanation

f(x)=x-[x]={x}

g(x)=1-x+[x]=1-{x}

Now, Graph of min {f(x),g(x)}

Clearly graph is continuous in [-2,2] but non differentiable at 7 points (i.e. greater than 4) in (-2,2)

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 2021, 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.