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Saturday, 31 October

JEE Main · Maths · Determinants

Determinant of Adjoint of Inverse

JEE Main asked Determinant of Adjoint of Inverse 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022 and 2024. It belongs to Matrix Inverse, in Determinants (Maths). The longest wait between two years asking it was 2 years. In 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 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.

00.050.10’170’200.07’210.07’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 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
  • 20222 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: multi-step.

  • Evaluate nested adjoint and inverse of matrix
  • Evaluate nested adjoint determinant

Difficulty

Easy 0Medium 5Hard 0

Every question was multiple choice.

Every question

All 5 questions

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

  1. 5 Apr 2024, Shift 1 · Q3Let A and B be two square matrices of order 3 such that ∣A∣=3|A|=3 and ∣B∣=2|B|=2. Then…MediumSingle correct
  2. 28 Jun 2022, Shift 1 · Q4Let AA be a matrix of order 3×33\times3 and det⁡(A)=2\det(A)=2. Then det⁡(det⁡(A) adj(5 adj(A3)))\det(\det(A)\,\mathrm{adj}(5\,\mathrm{adj}(A^3))) is equal to __________.MediumSingle correct
  3. 27 Jun 2022, Shift 2 · Q4Let AA and BB be two 3×33\times3 matrices such that AB=IAB=I and ∣A∣=18|A|=\frac{1}{8}. Then ∣adj (B adj(2A))∣|adj\,(B\,adj(2A))| is equal toMediumSingle correct
  4. 4 Aug 2021, Shift 2 · Q62If A is a 3×33\times3 matrix and ∣A∣=136|A|=\frac{1}{36}, then the value of ∣2⋅adj(3⋅adj(6A))∣|2\cdot adj(3\cdot adj(6A))| isMediumSingle correct
  5. 3 Aug 2021, Shift 1 · Q63Let A be a square matrix of order 3 and ∣A∣=3|A| = 3. If ∣Adj (3 Adj (4A))∣=2m⋅3n|\mathrm{Adj}\,(3\,\mathrm{Adj}\,(4A))| = 2^m \cdot 3^n, then the ordered pair…MediumSingle correct

Shifts: 3 Aug 2021, Shift 1, 4 Aug 2021, Shift 2, 27 Jun 2022, Shift 2, 28 Jun 2022, Shift 1, 5 Apr 2024, Shift 1.

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