JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Let

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

A^2 + A^3 + \ldots + A^{10}

is equal to :

(1) $\left(\frac{3^{10} - 3}{2}\right)A$ Official answer
(2) $\left(\frac{3^{10} - 1}{2}\right)A$
(3) $\left(\frac{3^{10} + 1}{2}\right)A$
(4) $\left(\frac{3^{10} + 3}{2}\right)A$

Official answer

Option 1

NTA final key (2022 Session 1).

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

Same idea in other shifts

Asked 21× in all

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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
6 Apr 2023, Shift 2 · Q4Let $P$ be a square matrix such that $P^2=I-P$ . For $\alpha,\beta,\gamma,\delta\in\mathbb{N}$ , if $P^\alpha+P^\beta=\gamma I-29P$ and…HardSingle correct
8 Apr 2023, Shift 1 · Q5Let $P=\begin{bmatrix}\frac{\sqrt{3}}{2}&\frac{1}{2}\\-\frac{1}{2}&\frac{\sqrt{3}}{2}\end{bmatrix}$ ,…HardSingle correct
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
12 Apr 2023, Shift 1 · Q3Let $A=\begin{bmatrix}1&\frac{1}{51}\\0&1\end{bmatrix}$ . If…HardSingle correct
25 Jul 2022, Shift 1 · Q21Let $A=\begin{pmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{pmatrix}$ and $B=A-I$ . If $\omega=\frac{\sqrt3\,i-1}{2}$ , then the number of elements in…HardNumerical 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.