JEE Main 2023MathematicsDeterminantsMediumMCQ

JEE Main 2023 — Determinants Question with Solution

JEE Main 2023 (06 Apr Shift 2)

Question

For the system of equations

x+y+z=6

x+2y+αz=10

x+3y+5z=β, which one of the following is NOT true?

Choose an option

Show full solutionCorrect option: D
Correct answer
DSystem has a unique solution for α=3, β≠14

Step-by-step explanation

Given, the system of equations

x+y+z=6

x+2y+αz=10

x+3y+5z=β

Now finding,

△=11112α135

⇒△=110-3α-5-α+3-2

⇒△=6-2α

Now for unique solution, △≠0⇒α≠3

So, for unique solution ⇒α≠3

But in option D, system has unique solution for α=3 which is completely wrong.

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About this question

This is a previous-year question from JEE Main 2023, 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.