JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Consider a matrix

A = \begin{bmatrix} \alpha & \beta & \gamma \\ \alpha^2 & \beta^2 & \gamma^2 \\ \beta + \gamma & \gamma + \alpha & \alpha + \beta \end{bmatrix}

, where

\alpha, \beta, \gamma

are three distinct natural numbers. If

\frac{\det\left(\operatorname{adj}\left(\operatorname{adj}\left(\operatorname{adj}\left(\operatorname{adj} A\right)\right)\right)\right)}{(\alpha - \beta)^{16}(\beta - \gamma)^{16}(\gamma - \alpha)^{16}} = 2^{32} \times 3^{16}

, then the number of such 3 - tuples

(\alpha, \beta, \gamma)

is __________.

Official answer

NTA final key.

Chapter: Determinants
Topic: Matrix Inverse
Idea tested: Inverse Relation to Double Adjoint

Same idea in other shifts

Asked 16× in all

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6 Apr 2024, Shift 2 · Q4If $A$ is a square matrix of order 3 such that $\det(A)=3$ and…MediumSingle correct
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31 Jan 2024, Shift 2 · Q22Let A be a $3\times3$ matrix and $\det(A)=2$ . If…MediumNumerical value

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.