JEE Main 2024MathematicsDeterminantsEasyMCQ

JEE Main 2024 — Determinants Question with Solution

JEE Main 2024 (01 Feb Shift 1)

Question

If the system of equations

2x+3y−z=5

x+αy+3z=−4

3x−y+βz=7

has infinitely many solutions, then 13αβ is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B1120

Step-by-step explanation

Given:

The system of equations,

2x+3y-z=5

x+αy+3z=-4

3x-y+βz=7 have many solutions,

So, △=△1=△2=△3

Now, finding △2=25-11-4337β=0

⇒2-4β-21-5β-9-17+12=0

⇒13β=-16

Now, finding △3=2351α-43-17=0

⇒14α-8-57-5-15α=0

⇒α=-70

Hence, the value of 13αβ=70×16=1120

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About this question

This is a previous-year question from JEE Main 2024, 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.