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Functions question

2024 · 6 Apr · Shift 2 · Q30

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PYQ Library
JEE Main
Mathematics
Functions
2024 · 6 Apr · Shift 2 · Q30

Functions question

2024 · 6 Apr · Shift 2 · Q30

JEE MainMathematicsFunctionsMCQ+4 / −1

If the function

f(x)=\left(\frac{1}{x}\right)^{2 x} ; x\gt 0

attains the maximum value at

x=\frac{1}{\mathrm{e}}

then :

A
$\mathrm{e}^\pi\lt \pi^{\mathrm{e}}$
B
$\mathrm{e}^{2 \pi}\lt (2 \pi)^{\mathrm{e}}$
C
$(2 e)^\pi\gt \pi^{(2 e)}$
D
$\mathrm{e}^\pi\gt \pi^{\mathrm{e}}$

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