JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2024, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

If the function

f(x)=\left(\frac{1}{x}\right)^{2x}

;

x>0

attains the maximum value at

x=\frac{1}{e}

then :

(1) $e^{\pi}>\pi^{e}$ Official answer
(2) $e^{\pi}<\pi^{e}$
(3) $e^{2\pi}<(2\pi)^{e}$
(4) $(2e)^{\pi}>\pi^{(2e)}$

Official answer

Option 1

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Extrema of x^x and x^(1/x)

Same topic in other shifts

All Maxima and Minima questions

2 Apr 2026, Shift 1 · Q18The number of critical points of the function $f(x)=\begin{cases}\left|\frac{\sin x}{x}\right|, & x\neq0\\ 1, & x=0\end{cases}$ in the…HardSingle correct
2 Apr 2026, Shift 2 · Q18Let $f(x)$ be a polynomial of degree 5, and have extrema at $x = 1$ and $x = -1$ . If $\lim_{x \to 0}\left(\frac{f(x)}{x^3}\right) = -5$ ,…MediumSingle correct
4 Apr 2026, Shift 2 · Q12 $\max_{0\le x\le\pi}\left(16\sin\left(\frac x2\right)\cos^3\left(\frac x2\right)\right)$ is equal to:MediumSingle correct
5 Apr 2026, Shift 1 · Q12The sum of all the integral values of $p$ such that the equation $3\sin^2 x + 12\cos x - 3 = p$ , $x \in \mathbb{R}$ , has at least one…MediumSingle correct
2 Apr 2025, Shift 1 · Q8If the function $f(x)=2x^3-9ax^2+12a^2x+1$ , where $a>0$ , attains its local maximum and local minimum values at p and q, respectively, such…MediumSingle correct
3 Apr 2025, Shift 2 · Q16Let $f: \mathrm{R} \to \mathrm{R}$ be a function defined by $f(x) = \left||x+2| - 2|x|\right|$ . If $m$ is the number of points of local…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 42 of the 174 JEE Main shifts held from 2017 to 2026.