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Saturday, 31 October

JEE Main · Maths · Sequences and Series

Arithmetic and Geometric Means

JEE Main asked Arithmetic and Geometric Means 4 times in 4 of the 108 shifts Lumi analysed, in 2020, 2021, 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
4
in 4 shifts
Years
4 of 8
First asked
2020
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.03’210.04’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 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
  • 20211 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: calculation.

  • Expression in geometric means between two numbers
  • Identity relating arithmetic and geometric means inserted

Difficulty

Easy 0Medium 4Hard 0

1 of the 4 questions had a numerical answer.

Every question

All 4 questions

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

  1. 15 Apr 2023, Shift 1 · Q8Let A1A_1 and A2A_2 be two arithmetic means and G1,G2,G3G_1, G_2, G_3 be three geometric means of two distinct positive numbers. Then…MediumSingle correct
  2. 28 Jun 2022, Shift 2 · Q5If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1:71:7 and a+n=33a+n=33, then…MediumSingle correct
  3. 3 Aug 2021, Shift 2 · Q67If 'mm' is the arithmetic mean of two distinct real numbers ll and nn (l,n>1)(l, n > 1) and G1G_1, G2G_2 and G3G_3 are three geometric means…MediumSingle correct
  4. 3 Sep 2020, Shift 2 · Q73If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th4^{th} A.M. is equal to 2nd2^{nd}…MediumNumerical value

Shifts: 3 Sep 2020, Shift 2, 3 Aug 2021, Shift 2, 28 Jun 2022, Shift 2, 15 Apr 2023, Shift 1.

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