JEE Main 2020 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 6 September 2020, Shift 2, Maths Q58

Question 58 of 75 in this shift, Maths question 8 of 25.

Let

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

f

is not differentiable. Then :

(1) $\phi$ (an empty set)
(2) $\{0,1\}$ Official answer
(3) $\{0\}$
(4) $\{1\}$

Official answer

Option 2

NTA final key (Sep 2020).

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

Same idea in other shifts

Asked 6× in all

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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
25 Feb 2021, Shift 2 · Q81A function $f$ is defined on $[-3, 3]$ as…HardNumerical 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.