JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q4

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

Let

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

C^4+\alpha C^2+\beta I=O

, then

2\beta-\alpha

is equal to

(1) $2$
(2) $8$
(3) $10$ Official answer
(4) $16$

Official answer

Option 3

NTA final key.

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

Same idea in other shifts

Asked 10× in all

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