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JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 26 August 2021, Shift 2, Maths Q66

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

The local maximum value of the function

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

,

x>0

, is :

(1) $(2\sqrt{\mathrm{e}})^{\frac{1}{\mathrm{e}}}$
(2) $(\mathrm{e})^{\frac{2}{\mathrm{e}}}$ Official answer
(3) $\left(\frac{4}{\sqrt{\mathrm{e}}}\right)^{\frac{\mathrm{e}}{4}}$
(4) $1$

Official answer

Option 2

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Extrema of Variable-Base Exponentials

Same idea in other shifts

Asked 2× in all

12 Apr 2023, Shift 1 · Q9If the local maximum value of the function $f(x)=\left(\frac{\sqrt{3e}}{2\sin x}\right)^{\sin^2 x}$ , $x\in\left(0,\frac{\pi}{2}\right)$ ,…HardSingle 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.