JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 28 July 2022, Shift 2, Maths Q66

Question 66 of 90 in this shift, Maths question 6 of 30, Section A.

The function

f(x)=xe^{x(1-x)},\ x\in\mathbb{R}

, is :

(1)increasing in $\left(-\frac{1}{2},1\right)$ Official answer
(2)decreasing in $\left(\frac{1}{2},2\right)$
(3)increasing in $\left(-1,-\frac{1}{2}\right)$
(4)decreasing in $\left(-\frac{1}{2},\frac{1}{2}\right)$

Official answer

Option 1

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Finding Intervals

Same idea in other shifts

Asked 7× in all

8 Apr 2025, Shift 2 · Q17Let the function $f(x) = \frac{x}{3} + \frac{3}{x} + 3$ , $x \neq 0$ be strictly increasing in…EasySingle correct
1 Feb 2024, Shift 1 · Q7If $5f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0$ and $y=9x^2f(x)$ , then $y$ is strictly increasing in :HardSingle correct
30 Jun 2022, Shift 1 · Q9Let $f(x) = 4x^3 - 11x^2 + 8x - 5$ , $x \in \mathbf{R}$ . Then $f$ :EasySingle correct
25 Jul 2021, Shift 1 · Q67Let $f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3$ , $x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]$ . Then, $f$ is :MediumSingle correct
16 Mar 2021, Shift 2 · Q64Let $f$ be a real valued function, defined on $\mathbf R-\{-1,1\}$ and given by $f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}$ .…MediumSingle correct
3 Sep 2020, Shift 1 · Q59The function, $f(x)=(3x-7)x^{2/3}$ , $x\in\mathbf{R}$ , is increasing for all $x$ lying in :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.