JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 27 July 2022, Shift 1, Maths Q4

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

Let

A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}

. Let

\alpha, \beta \in \mathbb{R}

be such that

\alpha A^2 + \beta A = 2I

. Then

\alpha + \beta

is equal to

(1) $-10$
(2) $-6$
(3)6
(4)10Official answer

Official answer

Option 4

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.