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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 26 August 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

Let [t][t] denote the greatest integer less than or equal to t. Let f(x)=x−[x]f(x)=x-[x], g(x)=1−x+[x]g(x)=1-x+[x], and h(x)=min⁡{f(x),g(x)}h(x)=\min\{f(x),g(x)\}, x∈[−2,2]x\in[-2,2]. Then h is :
  1. (1)not continuous at exactly four points in [−2,2][-2,2]
  2. (2)not continuous at exactly three points in [−2,2][-2,2]
  3. (3)continuous in [−2,2][-2,2] but not differentiable at more than four points in (−2,2)(-2,2)Official answer
  4. (4)Continous in [−2,2][-2,2] but not differentiable at exactly three poionts in (−2,2)(-2,2)

Official answer

Option 3

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
  1. 4 Apr 2026, Shift 1 · Q25The number of points, at which the function f(x)=max⁡{6x, 2+3x2}+∣x−1∣cos⁡∣x2−14∣f(x)=\max\{6x,\ 2+3x^2\}+|x-1|\cos\left|x^2-\frac14\right|, x∈(−π,π)x\in(-\pi,\pi), is not…HardNumerical value
  2. 15 Apr 2023, Shift 1 · Q9Let [x][x] denote the greatest integer function and f(x)=max⁡{1+x+[x],2+x,x+2[x]}f(x)=\max\{1+x+[x], 2+x, x+2[x]\}, 0≤x≤20\le x\le 2. Let mm be the number of points in…HardSingle correct
  3. 26 Jun 2022, Shift 2 · Q5Let f(x)=min⁡{1,1+xsin⁡x},0≤x≤2πf(x) = \min\{1, 1 + x \sin x\}, 0 \leq x \leq 2\pi. If mm is the number of points, where ff is not differentiable and nn is the…MediumSingle correct
  4. 25 Feb 2021, Shift 2 · Q81A function ff is defined on [−3,3][-3, 3] as…HardNumerical value
  5. 6 Sep 2020, Shift 2 · Q58Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a function defined by f(x)=max⁡{x,x2}f(x)=\max\{x,x^2\}. Let S denote the set of all points in R\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.