JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 1, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

Let

A=\begin{bmatrix}\alpha&-1\\6&\beta\end{bmatrix}

\alpha>0

, such that

\det(A)=0

and

\alpha+\beta=1

. If I denotes

2\times2

identity matrix, then the matrix

(I+A)^8

is :

(1) $\begin{bmatrix}4&-1\\6&-1\end{bmatrix}$
(2) $\begin{bmatrix}257&-64\\514&-127\end{bmatrix}$
(3) $\begin{bmatrix}766&-255\\1530&-509\end{bmatrix}$ Official answer
(4) $\begin{bmatrix}1025&-511\\2024&-1024\end{bmatrix}$

Official answer

Option 3

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Idempotent and Nilpotent Matrices

Same topic in other shifts

All Matrix Multiplication questions

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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 42 of the 174 JEE Main shifts held from 2017 to 2026.