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Saturday, 31 October

JEE Main · Maths · Matrices

Binomial Expansion for Commuting Matrices

JEE Main asked Binomial Expansion for Commuting Matrices 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2022 and 2026. It belongs to Matrix Multiplication, in Matrices (Maths). The longest wait between two years asking it was 4 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210.04’220’230’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 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
  • 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.

  • Entries of high matrix power
  • Sum of entries of matrix binomial expression

Difficulty

Easy 0Medium 3Hard 0

1 of the 3 questions had a numerical answer.

Every question

All 3 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 · Q5Let A=[100310931]A=\begin{bmatrix}1&0&0\\3&1&0\\9&3&1\end{bmatrix} and B=[bij]B=[b_{ij}], 1≤i,j≤31\le i,j\le 3. If B=A99−IB=A^{99}-I, then the value of…MediumSingle correct
  2. 29 Jun 2022, Shift 2 · Q3Let A=(2−102)A = \begin{pmatrix} 2 & -1 \\ 0 & 2 \end{pmatrix}. If B=I−5C1 (adjA)+5C2 (adjA)2−…−5C5 (adjA)5B = I - {}^5C_1\,(adjA) + {}^5C_2\,(adjA)^2 - \ldots - {}^5C_5\,(adjA)^5,…MediumSingle correct
  3. 31 Aug 2021, Shift 2 · Q81The number of elements in the set…MediumNumerical value

Shifts: 31 Aug 2021, Shift 2, 29 Jun 2022, Shift 2, 6 Apr 2026, Shift 2.

Same topic

Other ideas in Matrix Multiplication

Matrix Multiplication has 19 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas