JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

[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

[0,2]

, where

f

is not continuous and

n

be the number of points in

(0,2)

, where

f

is not differentiable. Then

(m+n)^2+2

is equal to

(1) $2$
(2) $3$ Official answer
(3) $6$
(4) $11$

Official answer

Option 2

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

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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
6 Sep 2020, Shift 2 · Q58Let $f:\mathbf{R}\to\mathbf{R}$ be a function defined by $f(x)=\max\{x,x^2\}$ . Let S denote the set of all points in $\mathbf{R}$ , where…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.