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Saturday, 31 October

JEE Main · Maths · Sequences and Series

Weighted AM-GM Inequality

JEE Main asked Weighted AM-GM Inequality 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2023. It belongs to AP and GP, in Sequences and Series (Maths). The longest wait between two years asking it was 1 year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2023
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210.04’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 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
  • 20221 of 24
  • 20210 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: application.

  • Maximum of weighted product under sum constraint
  • Minimum value using am-gm

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. 11 Apr 2023, Shift 2 · Q9Let a,b,ca, b, c and dd be positive real numbers such that a+b+c+d=11a + b + c + d = 11. If the maximum value of a5b3c2da^5 b^3 c^2 d is 3750β3750\beta,…MediumSingle correct
  2. 24 Jun 2022, Shift 2 · Q4Let x,y>0x, y > 0. If x3y2=215x^3y^2 = 2^{15}, then the least value of 3x+2y3x + 2y isMediumSingle correct

Shifts: 24 Jun 2022, Shift 2, 11 Apr 2023, 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