JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

Let

A=\begin{bmatrix}2&a&0\\1&3&1\\0&5&b\end{bmatrix}

. If

A^3=4A^2-A-21I

, where

I

is the identity matrix of order

3\times3

, then

2a+3b

is equal to

(1) $-9$
(2) $-13$ Official answer
(3) $-12$
(4) $-10$

Official answer

Option 2

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Cayley-Hamilton Theorem Application

Same idea in other shifts

Asked 4× in all

2 Apr 2026, Shift 1 · Q4Let $A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix}$ and $B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}$ . If $A^2-4A+I=O$ and $B^2-5B-6I=O$ ,…HardOther
2 Apr 2025, Shift 2 · Q3Let $A$ be a $3\times3$ real matrix such that $A^2(A-2I) - 4(A-I) = O$ , where $I$ and $O$ are the identity and null matrices,…MediumSingle correct
9 Apr 2024, Shift 2 · Q4Let $B=\begin{bmatrix}1&3\\1&5\end{bmatrix}$ and $A$ be a $2\times2$ matrix such that $AB^{-1}=A^{-1}$ . If $BCB^{-1}=A$ and…HardSingle correct

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.