Learn

Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Cyclic Powers of Omega Modulo 3

JEE Main asked Cyclic Powers of Omega Modulo 3 2 times in 2 of the 108 shifts Lumi analysed, in 2021 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
2
in 2 shifts
Years
2 of 8
First asked
2021
last in 2025
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • N from sum over cube root powers
  • Sum of series from roots of quadratic

Difficulty

Easy 0Medium 2Hard 0

2 of the 2 questions had a numerical answer.

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. 4 Apr 2025, Shift 2 · Q21If α\alpha is a root of the equation x2+x+1=0x^2+x+1=0 and ∑k=1n(αk+1αk)2=20\sum_{k=1}^{n}\left(\alpha^k+\frac{1}{\alpha^k}\right)^2=20, then n is equal to…MediumNumerical value
  2. 3 Aug 2021, Shift 1 · Q81If x2−x+1=0x^2 - x + 1 = 0, then the value of ∑n=15(xn+1xn)2\sum_{n=1}^{5}\left(x^n + \frac{1}{x^n}\right)^2 is ________.MediumNumerical value

Shifts: 3 Aug 2021, Shift 1, 4 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