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Saturday, 31 October

JEE Main · Maths · Sequences and Series

AM-GM Inequality Application

JEE Main asked AM-GM Inequality Application 2 times in 2 of the 108 shifts Lumi analysed, in 2020 and 2024. It belongs to AP and GP, in Sequences and Series (Maths). The longest wait between two years asking it was 4 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2020
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170.08’200’210’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 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
  • 20220 of 24
  • 20210 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: multi-step.

  • Minimum value of term in ap
  • Least value from am-gm and ap condition

Difficulty

Easy 0Medium 2Hard 0

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. 5 Apr 2024, Shift 2 · Q8For x≥0x \geq 0, the least value of KK, for which 41+x+41−x4^{1+x}+4^{1-x}, K2\frac{K}{2}, 16x+16−x16^x+16^{-x} are three consecutive terms of an A.P.,…MediumSingle correct
  2. 8 Jan 2020, Shift 1 · Q56Let f:R→Rf:\mathbf{R}\to\mathbf{R} be such that for all x∈Rx\in\mathbf{R}, (21+x+21−x)(2^{1+x}+2^{1-x}), f(x)f(x) and (3x+3−x)(3^x+3^{-x}) are in A.P., then…MediumSingle correct

Shifts: 8 Jan 2020, Shift 1, 5 Apr 2024, Shift 2.

Same topic

Other ideas in AP and GP

AP and GP has 23 ideas JEE Main has asked; 16 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas