JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Let

A=\begin{pmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{pmatrix}

and

B=A-I

. If

\omega=\frac{\sqrt3\,i-1}{2}

, then the number of elements in the set

\{n\in\{1,2,\dots,100\}:A^n+(\omega B)^n=A+B\}

is equal to ______.

Official answer

NTA final key (2022 Session 2).

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

Same idea in other shifts

Asked 6× in all

4 Apr 2025, Shift 2 · Q4Let the matrix $A=\begin{bmatrix}1&0&0\\1&0&1\\0&1&0\end{bmatrix}$ satisfy $A^n=A^{n-2}+A^2-I$ for $n\ge 3$ . Then the sum of all the…HardSingle correct
8 Apr 2024, Shift 1 · Q22Let $A=\begin{bmatrix}2&-1\\1&1\end{bmatrix}$ . If the sum of the diagonal elements of $A^{13}$ is $3^n$ , then $n$ is equal to ____________.MediumNumerical value
11 Apr 2023, Shift 1 · Q29Let $A = \begin{bmatrix} 0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0 \end{bmatrix}$ , where $a, c \in \mathbb{R}$ . If $A^3 = A$ and the positive…HardNumerical value
29 Jun 2022, Shift 1 · Q10Let $A = [a_{ij}]$ be a square matrix of order 3 such that $a_{ij} = 2^{j-i}$ , for all $i, j = 1, 2, 3$ . Then, the matrix…MediumSingle correct
25 Jul 2021, Shift 1 · Q87Let…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 42 of the 174 JEE Main shifts held from 2017 to 2026.