JEE Main 2021 · MathsMultiple choiceSingle correctHardConceptual

JEE Main 17 March 2021, Shift 2, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

Consider the function

f:\mathbf{R}\to\mathbf{R}

defined by

f(x)=\begin{cases}\left(2-\sin\left(\frac{1}{x}\right)\right)|x|, & x\neq 0\\ 0, & x=0\end{cases}

. Then

f

is :

(1)monotonic on $(0, \infty)$ only
(2)monotonic on $(-\infty, 0)$ only
(3)monotonic on $(-\infty, 0)\cup(0, \infty)$
(4)not monotonic on $(-\infty, 0)$ and $(0, \infty)$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: First Derivative Test

Same idea in other shifts

Asked 4× in all

24 Jun 2022, Shift 1 · Q10For the function $f(x)=4\log_e(x-1)-2x^2+4x+5,\ x>1$ , which one of the following is NOT correct ?HardSingle correct
24 Feb 2021, Shift 1 · Q67The function $f(x) = \frac{4x^3 - 3x^2}{6} - 2\sin x + (2x - 1)\cos x$ :MediumSingle correct
2 Sep 2020, Shift 2 · Q61Let $f:(-1,\infty)\to\mathbf{R}$ be defined by $f(0)=1$ and $f(x)=\frac{1}{x}\log_e(1+x)$ , $x\neq 0$ . Then the function $f$ :MediumSingle 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.