JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 3 August 2021, Shift 1, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

Let

A = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{pmatrix}

and

B = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix}

. Then the set

\{n \in \mathbb{N} \mid A^n + A^{n+1} + A^{n+2} = B\}

(1)an empty set
(2)a finite set
(3)a proper infinite subset of $\mathbb{N}$
(4)equal to $\mathbb{N}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Powers of Square Matrices

Same idea in other shifts

Asked 21× in all

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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.