JEE Main 2022MathematicsDeterminantsEasyMCQ

JEE Main 2022 — Determinants Question with Solution

JEE Main 2022 (27 Jun Shift 1)

Question

Let the system of linear equations x+2y+z=2, αx+3y-z=α,-αx+y+2z=-α be inconsistent. Then α is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D-72

Step-by-step explanation

Given, the system of linear equations x+2y+z=2, αx+3y-z=α, and -αx+y+2z=-α 

Now for system to be inconsistent, ∆=0 & either of  ∆1,∆2 or ∆3 ≠0

So, Δ=12123-1-212

=6+y-22α-α+1α+3α

=7-2α+4α

=7+2α

Δ=0⇒α=-72

Now calculating, Δ1=221α3-1-α12

=14+2α

Where α=-72 so, ∆1=14-7=7

Δ1≠0, hence system is inconsistent at α=-72

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About this question

This is a previous-year question from JEE Main 2022, 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.