JEE Main 2019MathematicsDeterminantsEasyMCQ

JEE Main 2019 — Determinants Question with Solution

JEE Main 2019 (12 Jan Shift 1)

Question

An ordered pair α, β for which the system of linear equations
1+αx+βy+z=2
αx+1+βy+z=3
αx+βy+2z=2 has a unique solution, is :

Choose an option

Show full solutionCorrect option: C
Correct answer
C2, 4

Step-by-step explanation

For unique solution 1+αβ1α1+β1αβ2≠0

Applying C1→C1+C2+C3, we get

α+β+2β1α+β+21+β1α+β+2β2≠0

⇒α+β+21β111+β11β2≠0

⇒α+β+2≠0

Clearly, point 2, 4 satisfying the given condition.

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About this question

This is a previous-year question from JEE Main 2019, 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.