JEE Main 2024 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 6 April 2024, Shift 1, Maths Q9

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

The interval in which the function

f(x)=x^x

x>0

, is strictly increasing is

(1) $\left[\frac{1}{e},\infty\right)$ Official answer
(2) $\left(0,\frac{1}{e}\right]$
(3) $\left[\frac{1}{e^2},1\right)$
(4) $(0,\infty)$

Official answer

Option 1

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Monotonicity of Variable Exponent Functions

Same topic in other shifts

All Monotonicity questions

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
5 Apr 2024, Shift 1 · Q5For the function $f(x)=\sin x+3x-\frac{2}{\pi}(x^2+x)$ , where $x\in\left[0,\frac{\pi}{2}\right]$ , consider the following two statements :…MediumTwo statements
8 Apr 2024, Shift 1 · Q7For the function $f(x)=(\cos x)-x+1$ , $x\in\mathbb{R}$ , between the following two statements (S1) $f(x)=0$ for only one value of $x$ in…MediumTwo statements
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
10 Apr 2023, Shift 2 · Q9Let $g(x) = f(x) + f(1-x)$ and $f''(x) > 0,\ x \in (0,1)$ . If $g$ is decreasing in the interval $(0, \alpha)$ and increasing in the…HardSingle correct
11 Apr 2023, Shift 1 · Q10Let $f : [2, 4] \to \mathbb{R}$ be a differentiable function such that $(x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]$ …HardTwo statements

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.