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Saturday, 31 October

JEE Main · Maths · Determinants

Condition for Unique Solution

JEE Main asked Condition for Unique Solution 4 times in 4 of the 108 shifts Lumi analysed, in 2021, 2022 and 2024. It belongs to Cramer's Rule, in Determinants (Maths). The longest wait between two years asking it was 2 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
3 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.07’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20212 of 24
  • 20200 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: application.

  • Number of solutions of linear system
  • Unique solution then collinearity condition

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. 31 Jan 2024, Shift 2 · Q4Let AA be a 3×33\times3 real matrix such that A(101)=2(101)A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix},…MediumSingle correct
  2. 24 Jun 2022, Shift 2 · Q3Let the system of linear equations x+y+αz=2x + y + \alpha z = 2 3x+y+z=43x + y + z = 4 x+2z=1x + 2z = 1 have a unique solution (x∗,y∗,z∗)(x^*, y^*, z^*). If…MediumSingle correct
  3. 25 Feb 2021, Shift 2 · Q63The following system of linear equations 2x+3y+2z=92x + 3y + 2z = 9 3x+2y+2z=93x + 2y + 2z = 9 x−y+4z=8x - y + 4z = 8EasySingle correct
  4. 24 Feb 2021, Shift 2 · Q72For the system of linear equations : x−2y=1x-2y=1, x−y+kz=−2x-y+kz=-2, ky+4z=6ky+4z=6, k∈k\in R, consider the following statements : (A) The system has…MediumOther

Shifts: 24 Feb 2021, Shift 2, 25 Feb 2021, Shift 2, 24 Jun 2022, Shift 2, 31 Jan 2024, 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