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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Let 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, then the sum of all elements of the matrix BB is
  1. (1)−5-5
  2. (2)−6-6
  3. (3)−7-7Official answer
  4. (4)−8-8

Official answer

Option 3

NTA final key.

Chapter
Determinants
Topic
Matrix Multiplication
Idea tested
Binomial Expansion for Commuting Matrices

Same idea in other shifts

Asked 3× in all
  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. 31 Aug 2021, Shift 2 · Q81The number of elements in the set…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.