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JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q4

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

If

A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix}

,

A^{-1} = \alpha A + \beta I

and

\alpha + \beta = -2

, then

4\alpha^2 + \beta^2 + \lambda^2

is equal to :

(1)10
(2)12
(3)14Official answer
(4)19

Official answer

Option 3

NTA final key.

Chapter: Matrices
Topic: Matrix Inverse
Idea tested: Inverse via Characteristic Equation

Same idea in other shifts

Asked 2× in all

8 Jan 2020, Shift 2 · Q54If $A = \begin{pmatrix} 2 & 2 \\ 9 & 4 \end{pmatrix}$ and $I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ , then $10A^{-1}$ is equal to :EasySingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.