JEE Main 2021 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 25 February 2021, Shift 1, Maths Q86

Question 86 of 90 in this shift, Maths question 26 of 30, Section B.

The number of points, at which the function

f(x) = |2x+1| - 3|x+2| + |x^2 + x - 2|

x \in \mathrm{R}

is not differentiable, is __________.

Official answer

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Differentiability of Modulus Functions

Same idea in other shifts

Asked 9× in all

4 Apr 2026, Shift 2 · Q22Let $f(x)=\begin{cases}e^{x-1}, & x<0\\ x^2-5x+6, & x\ge0\end{cases}$ and $g(x)=f(|x|)+|f(x)|$ . If the number of points where $g$ is not…MediumNumerical value
1 Feb 2024, Shift 2 · Q8Let $f(x)=|2x^2+5|x|-3|$ , $x\in\mathbf{R}$ . If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable…MediumSingle correct
31 Jan 2024, Shift 2 · Q8Consider the function $f:(0,\infty)\to\mathbb{R}$ defined by $f(x)=e^{-|\log_e x|}$ . If $m$ and $n$ be respectively the number of points…MediumSingle correct
10 Apr 2023, Shift 1 · Q27Let $f:(-2,2)\to\mathbb{R}$ be defined by $f(x)=\begin{cases}x[x], & -2<x<0\\ (x-1)[x], & 0\le x<2\end{cases}$ where $[x]$ denotes the…HardNumerical value
27 Jul 2022, Shift 2 · Q6Let $f(x) = 2 + |x| - |x - 1| + |x + 1|$ , $x \in \mathbf{R}$ . Consider (S1) :…MediumTwo statements
29 Jul 2022, Shift 1 · Q18The number of points, where the function $f : \mathbf{R} \to \mathbf{R}$ , $f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|$ ,…HardSingle correct
4 Aug 2021, Shift 1 · Q89The number of points in $(0, 2\pi)$ , where the function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x)=|\sin x|+|\cos x|$ is NOT…MediumNumerical value
31 Aug 2021, Shift 1 · Q69The function $f(x)=|x^2-2x-3|\cdot\mathrm{e}^{|9x^2-12x+4|}$ is not differentiable at exactly :MediumSingle 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.