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Saturday, 31 October

JEE Main · Maths · Determinants

Homogeneous System Solutions

JEE Main asked Homogeneous System Solutions 4 times in 4 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2026. It belongs to Cramer's Rule, in Determinants (Maths). The longest wait between two years asking it was 4 years.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
4 of 8
First asked
2020
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.08’200.03’210.04’220’230’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 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: multi-step.

  • Nature of solutions of homogeneous system
  • Non-trivial solution then sum trig roots

Difficulty

Easy 1Medium 3Hard 0

Every question was multiple choice.

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. 6 Apr 2026, Shift 2 · Q4The sum of all possible values of θ∈[0,2π]\theta\in[0,2\pi], for which the system of equations : xcos⁡3θ−8y−12z=0x\cos 3\theta-8y-12z=0…MediumSingle correct
  2. 29 Jul 2022, Shift 1 · Q3Let A and B be two 3×33 \times 3 non-zero real matrices such that AB is a zero matrix. ThenMediumSingle correct
  3. 31 Aug 2021, Shift 2 · Q64If α+β+γ=2π\alpha+\beta+\gamma = 2\pi, then the system of equations x+(cos⁡γ)y+(cos⁡β)z=0x+(\cos\gamma)y+(\cos\beta)z = 0 (cos⁡γ)x+y+(cos⁡α)z=0(\cos\gamma)x+y+(\cos\alpha)z = 0…MediumSingle correct
  4. 9 Jan 2020, Shift 2 · Q55The following system of linear equations 7x+6y−2z=07x+6y-2z=0 3x+4y+2z=03x+4y+2z=0 x−2y−6z=0x-2y-6z=0, hasEasySingle correct

Shifts: 9 Jan 2020, Shift 2, 31 Aug 2021, Shift 2, 29 Jul 2022, Shift 1, 6 Apr 2026, Shift 2.

Same topic

Other ideas in Cramer's Rule

Cramer's Rule has 19 ideas JEE Main has asked; 6 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas