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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Optimization via AM-GM Inequality

JEE Main asked Optimization via AM-GM Inequality 5 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2024. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 2 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
4 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.07’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20212 of 24
  • 20201 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: application.

  • Minimum of sum of intercepts of line
  • Unknown constant from given minimum value

Difficulty

Easy 0Medium 5Hard 0

1 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 31 Jan 2024, Shift 2 · Q10Let a variable line passing through the centre of the circle x2+y2−16x−4y=0x^2+y^2-16x-4y=0, meet the positive co-ordinate axes at the points AA and…MediumSingle correct
  2. 28 Jul 2022, Shift 1 · Q17If the minimum value of f(x)=5x22+αx5, x>0f(x)=\frac{5x^2}{2}+\frac{\alpha}{x^5},\ x>0, is 14, then the value of α\alpha is equal to :MediumSingle correct
  3. 25 Feb 2021, Shift 2 · Q67The minimum value of f(x)=aax+a1−axf(x) = a^{a^x} + a^{1-a^x}, where a,x∈Ra, x \in \mathbf{R} and a>0a > 0, is equal to :MediumSingle correct
  4. 24 Feb 2021, Shift 1 · Q86The minimum value of α\alpha for which the equation 4sin⁡x+11−sin⁡x=α\frac{4}{\sin x} + \frac{1}{1 - \sin x} = \alpha has at least one solution in…MediumNumerical value
  5. 4 Sep 2020, Shift 2 · Q60The minimum value of 2sin⁡x+2cos⁡x2^{\sin x} + 2^{\cos x} is :MediumSingle correct

Shifts: 4 Sep 2020, Shift 2, 24 Feb 2021, Shift 1, 25 Feb 2021, Shift 2, 28 Jul 2022, Shift 1, 31 Jan 2024, Shift 2.

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