JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 February 2021, Shift 2, Maths Q81

Question 81 of 90 in this shift, Maths question 21 of 30, Section B.

A function

f

is defined on

[-3, 3]

f(x) = \begin{cases} \min\{|x|, 2 - x^2\}, & -2 \leq x \leq 2 \\ [|x|], & 2 < |x| \leq 3 \end{cases}

where

[x]

denotes the greatest integer

\leq x

. The number of points, where

f

is not differentiable in

(-3, 3)

is ________.

Official answer

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Differentiability of Max/Min Functions

Same idea in other shifts

Asked 6× in all

4 Apr 2026, Shift 1 · Q25The number of points, at which the function $f(x)=\max\{6x,\ 2+3x^2\}+|x-1|\cos\left|x^2-\frac14\right|$ , $x\in(-\pi,\pi)$ , is not…HardNumerical value
15 Apr 2023, Shift 1 · Q9Let $[x]$ denote the greatest integer function and $f(x)=\max\{1+x+[x], 2+x, x+2[x]\}$ , $0\le x\le 2$ . Let $m$ be the number of points in…HardSingle correct
26 Jun 2022, Shift 2 · Q5Let $f(x) = \min\{1, 1 + x \sin x\}, 0 \leq x \leq 2\pi$ . If $m$ is the number of points, where $f$ is not differentiable and $n$ is the…MediumSingle correct
26 Aug 2021, Shift 2 · Q76Let $[t]$ denote the greatest integer less than or equal to t. Let $f(x)=x-[x]$ , $g(x)=1-x+[x]$ , and $h(x)=\min\{f(x),g(x)\}$ ,…MediumSingle correct
6 Sep 2020, Shift 2 · Q58Let $f:\mathbf{R}\to\mathbf{R}$ be a function defined by $f(x)=\max\{x,x^2\}$ . Let S denote the set of all points in $\mathbf{R}$ , where…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.