JEE Main 2021 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 4 August 2021, Shift 1, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

The 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 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
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.