JEE Main 2021MathematicsDeterminantsEasyNumerical

JEE Main 2021 — Determinants Question with Solution

JEE Main 2021 (27 Jul Shift 1)

Question

For real numbers α and β, consider the following system of linear equations: x+y-z=2, x+2y+αz=1 and 2x-y+z=β. If the system has infinite solutions, then α+β is equal to ______.

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Show full solutionCorrect answer: 5
Correct answer
5

Step-by-step explanation

Given system of linear equations are x+y-z=2,x+2y+αz=1,2x-y+z=β

Using Cramer Rule, we can say for infinite solutions

Δ=Δ1=Δ2=Δ3=0

Here, Δ=11-112α2-11=0

Apply R1↔R1+R3

⇒30012α2-11=0

⇒32+α=0

⇒α=-2

And Δ2=12-111-22β1=0

⇒11+2β-21+4-β-2=0

⇒β-7=0

⇒β=7

∴ α+β=5

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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.