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Saturday, 31 October

JEE Main · Maths · Determinants

Cofactor Matrix and Adjoint

JEE Main asked Cofactor Matrix and Adjoint 6 times in 6 of the 108 shifts Lumi analysed, in 2017, 2021, 2022, 2024 and 2026. It belongs to Matrix Inverse, in Determinants (Maths). The longest wait between two years asking it was 4 years, across 2018 and 2019, which Lumi has no shifts for. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
5 of 8
First asked
2017
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

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

00.510.86’170’200.07’210.04’220’230.05’240’250.11’26

Raw count: 2017: 1 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: 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
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20212 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: multi-step.

  • Evaluate nested adjoint and inverse of matrix
  • Determinant involving adjoint matrix

Difficulty

Easy 0Medium 4Hard 2

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 8 Apr 2026, Shift 2 · Q4Let A=[α12230045]A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix} and…HardSingle correct
  2. 5 Apr 2024, Shift 2 · Q5Let αβ≠0\alpha\beta \neq 0 and…MediumSingle correct
  3. 26 Jul 2022, Shift 1 · Q4Let A be a 2×22 \times 2 matrix with det⁡ (A)=−1\det\,(\mathrm{A}) = -1 and…HardSingle correct
  4. 17 Mar 2021, Shift 1 · Q82If A =[230−1]=\begin{bmatrix}2 & 3\\ 0 & -1\end{bmatrix}, then the value of det⁡(A4)+det⁡(A10−(Adj(2A))10)\det(A^{4})+\det\left(A^{10}-(\mathrm{Adj}(2A))^{10}\right) is…MediumNumerical value
  5. 4 Aug 2021, Shift 1 · Q63Let A=[x321y422z]A=\begin{bmatrix}x&3&2\\1&y&4\\2&2&z\end{bmatrix}, xyz=60xyz=60 and 8x+4y+3z=208x+4y+3z=20. If A(adj A)=k IA(adj\ A)=k\,I, then kk is equal toMediumSingle correct
  6. 2 Apr 2017 (offline) · Q64If A=[2−3−41]A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}, then adj(3A2+12A)\mathrm{adj}(3A^2+12A) is equal to :MediumSingle correct

Shifts: 2 Apr 2017 (offline), 17 Mar 2021, Shift 1, 4 Aug 2021, Shift 1, 26 Jul 2022, Shift 1, 5 Apr 2024, Shift 2, 8 Apr 2026, Shift 2.

Same topic

Other ideas in Matrix Inverse

Matrix Inverse has 14 ideas JEE Main has asked; 7 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas