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Saturday, 31 October

JEE Main · Maths · Determinants

Evaluating Determinants with Cube Roots

JEE Main asked Evaluating Determinants with Cube Roots 2 times in 2 of the 108 shifts Lumi analysed, in 2017 and 2021. It belongs to Roots of Unity, in Determinants (Maths). The longest wait between two years asking it was 4 years, across 2018 and 2019, which Lumi has no shifts for.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2017
last in 2021
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

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

00.510.86’170’200.03’210’220’230’240’250’26

Raw count: 2017: 1 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: 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
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20200 of 12
  • 20171 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.

  • Determinant with cube root of unity entries
  • Determinant with roots of unity entries

Difficulty

Easy 0Medium 1Hard 1

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. 31 Aug 2021, Shift 1 · Q63If ar=cos⁡2rπ9+isin⁡2rπ9\mathrm{a_r}=\cos\frac{2\mathrm{r}\pi}{9}+i\sin\frac{2\mathrm{r}\pi}{9}, r=1,2,3,...,i=−1\mathrm{r}=1, 2, 3, ..., i=\sqrt{-1}, then the determinant…HardSingle correct
  2. 2 Apr 2017 (offline) · Q63Let ω\omega be a complex number such that 2ω+1=z2\omega+1=z where z=−3z=\sqrt{-3}. If…MediumSingle correct

Shifts: 2 Apr 2017 (offline), 31 Aug 2021, Shift 1.

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