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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Periodicity of Omega Powers

JEE Main asked Periodicity of Omega Powers 3 times in 3 of the 108 shifts Lumi analysed, in 2020, 2024 and 2025. It belongs to Roots of Unity, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 4 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2020
last in 2025
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200’210’220’230.05’240.13’250’26

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: 1 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
  • 20251 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.

  • Find unknowns from matrix equation then omega powers
  • Reduce power of expression in cube root of unity

Difficulty

Easy 0Medium 3Hard 0

1 of the 3 questions had a numerical answer.

Every question

All 3 questions

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

  1. 8 Apr 2025, Shift 2 · Q5Let α\alpha be a solution of x2+x+1=0x^2 + x + 1 = 0, and for some aa and bb in R\mathbb{R},…MediumSingle correct
  2. 27 Jan 2024, Shift 1 · Q21If α\alpha satisfies the equation x2+x+1=0x^2+x+1=0 and (1+α)7=A+Bα+Cα2(1+\alpha)^7=A+B\alpha+C\alpha^2, A,B,C≥0A, B, C\geq 0, then 5(3A−2B−C)5(3A-2B-C) is equal to…MediumNumerical value
  3. 8 Jan 2020, Shift 2 · Q52Let α=−1+i32\alpha = \frac{-1 + i\sqrt{3}}{2}. If a=(1+α)∑k=0100α2ka = (1 + \alpha) \sum_{k=0}^{100} \alpha^{2k} and b=∑k=0100α3kb = \sum_{k=0}^{100} \alpha^{3k}, then a…MediumSingle correct

Shifts: 8 Jan 2020, Shift 2, 27 Jan 2024, Shift 1, 8 Apr 2025, Shift 2.

Same topic

Other ideas in Roots of Unity

Roots of Unity has 11 ideas JEE Main has asked; 6 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas