JEE Main 2023MathematicsDeterminantsMediumMCQ

JEE Main 2023 — Determinants Question with Solution

JEE Main 2023 (10 Apr Shift 1)

Question

For the system of linear equations

2x-y+3z=5

3x+2y-z=7

4x+5y+αz=β,

which of the following is NOT correct?

Choose an option

Show full solutionCorrect option: B
Correct answer
BThe system has infinitely many solutions for α=-6 and β=9

Step-by-step explanation

Given,

For the system of linear equations

2x-y+3z=5

3x+2y-z=7

4x+5y+αz=β,

Now finding,

D=2-1332-145α

⇒D=22α+5+3α+4+37

⇒D=7α+35

Now we know that, for unique solutionD≠0⇒α≠–5

So, in option B α=–6 corresponds to infinitely many solution, which is completely wrong hence, this is answer.

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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.