JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

The 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|

, is NOT differentiable, is :

(1)1
(2)2Official answer
(3)3
(4)4

Official answer

Option 2

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
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
25 Feb 2021, Shift 1 · Q86The 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…MediumNumerical value

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.