JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 4 August 2021, Shift 2, Maths Q83

Question 83 of 90 in this shift, Maths question 23 of 30, Section B.

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

, the sum of the entries of

A^{20}

is ________ .

Official answer

253

NTA final key.

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

Same idea in other shifts

Asked 21× 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
4 Apr 2024, Shift 2 · Q3Let $A=\begin{bmatrix}1&2\\0&1\end{bmatrix}$ and $B=I+\mathrm{adj}(A)+(\mathrm{adj}\,A)^2+\ldots+(\mathrm{adj}\,A)^{10}$ . Then, the sum of…MediumSingle 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
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.