JEE Main 2021MathematicsDeterminantsHardMCQ

JEE Main 2021 — Determinants Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

Let [λ] be the greatest integer less than or equal to λ. The set of all values of λ for which the system of linear equations x+y+z=4, 3x+2y+5z=3, 9x+4y+(28+[λ])z=[λ] has a solution is:

Choose an option

Show full solutionCorrect option: A
Correct answer
AR

Step-by-step explanation

Given, the system of linear equations, 

x+y+z=4 ........................i

3x+2y+5z=3................ii

9x+4y+(28+[λ]]z=[λ].....................iii

D=1113259428+[λ]

=156+2λ-20-184+3λ-45+112-18 

D=−([λ]+9)

If D=-[λ]+9≠0 then unique solution
If D=-[λ]+9=0 then D1=D2=D3=0 infinite solutions

Hence,  λ∈R

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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.