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JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 12 April 2023, Shift 1, Maths Q9

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

If 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)

, is

\frac{k}{e}

, then

\left(\frac{k}{e}\right)^8+\frac{k^8}{e^5}+k^8

is equal to

(1) $e^5+e^6+e^{11}$
(2) $e^3+e^6+e^{10}$
(3) $e^3+e^5+e^{11}$
(4) $e^3+e^6+e^{11}$ Official answer

Official answer

Option 4

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

26 Aug 2021, Shift 2 · Q66The local maximum value of the function $f(x)=\left(\frac{2}{x}\right)^{x^2}$ , $x>0$ , is :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.