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Saturday, 31 October

JEE Main · Maths · Determinants

Geometric Meaning of Non-Trivial Homogeneous Solutions

JEE Main asked Geometric Meaning of Non-Trivial Homogeneous Solutions once in the 108 shifts Lumi analysed, on 2 Sep 2020, Shift 2. It belongs to Cramer's Rule, in Determinants (Maths).

Updated 2026-10-24

Times asked
1
in 1 shift
Years
1 of 8
First asked
2020
the only year
Pattern
Gone quiet
asked once so far

Questions on this idea a shift, by year

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

00.050.10’170.08’200’210’220’230’240’250’26

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: 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
  • 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: conceptual.

  • Count solutions of homogeneous system with norm

Difficulty

Easy 0Medium 1Hard 0

The question was multiple choice.

Every question

The question

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

  1. 2 Sep 2020, Shift 2 · Q55Let A={X=(x, y, z)T:PX=0A=\{X=(x,\ y,\ z)^T : PX=0 and x2+y2+z2=1}x^2+y^2+z^2=1\}, where P=[121−23−419−1]P=\begin{bmatrix} 1 & 2 & 1 \\ -2 & 3 & -4 \\ 1 & 9 & -1 \end{bmatrix},…MediumSingle correct

Shift: 2 Sep 2020, 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