JEE Main 2021MathematicsDeterminantsMediumMCQ

JEE Main 2021 — Determinants Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

Let A=[x+1][x+2]  [x+3][x] [x+3]  [x+3][x][x+2] [x+4], where [x] denotes the greatest integer less than or equal to x. If det(A)=192, then the set of values of x is in the interval:

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Show full solutionCorrect option: A
Correct answer
A[62,63)

Step-by-step explanation

Given, A=[x+1][x+2][x+3][x][x+3][x+3][x][x+2][x+4]

A=[x]+1[x]+2[x]+3[x][x]+3[x]+3[x][x]+2[x]+4

R1→R1−R3,R2→R2−R3

A=10−101−1[x][x]+2[x]+4

det⁡(A)=1([x]+4+[x]+2)−1(−[x])

=3[x]+6

Given, det(A)=192

192=3[x]+6

3[x]=186

[x]=62

x∈[62,63)

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About this question

This is a previous-year question from JEE Main 2021, covering the Determinants chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.