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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Extrema of Variable-Base Exponentials

JEE Main asked Extrema of Variable-Base Exponentials 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2023. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2021
last in 2023
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20231 of 12
  • 20220 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Local maximum of variable-base exponential function
  • Local extremum of variable-base exponential function

Difficulty

Easy 0Medium 1Hard 1

Every question was multiple choice.

Every question

All 2 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 12 Apr 2023, Shift 1 · Q9If the local maximum value of the function f(x)=(3e2sin⁡x)sin⁡2xf(x)=\left(\frac{\sqrt{3e}}{2\sin x}\right)^{\sin^2 x}, x∈(0,π2)x\in\left(0,\frac{\pi}{2}\right),…HardSingle correct
  2. 26 Aug 2021, Shift 2 · Q66The local maximum value of the function f(x)=(2x)x2f(x)=\left(\frac{2}{x}\right)^{x^2}, x>0x>0, is :MediumSingle correct

Shifts: 26 Aug 2021, Shift 2, 12 Apr 2023, Shift 1.

Same topic

Other ideas in Maxima and Minima

Maxima and Minima has 31 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas