JEE Main 2019MathematicsDeterminantsMediumMCQ

JEE Main 2019 — Determinants Question with Solution

JEE Main 2019 (09 Jan Shift 1)

Question

The system of linear equations
x+y+z=2
2x+3y+2z=5
2x+3y+a2-1z=a+1

Choose an option

Show full solutionCorrect option: A
Correct answer
Ais inconsistent when a=3

Step-by-step explanation

Here, D=11123223a2-1

=a2-3

Hence at |a|=3 , D=0 . So system don't have unique solution.

At a=4 , D≠0 , So, system has unique solution. Hence not inconsistent.

At |a|=3,D=0 and 2nd & 3rd equation are parallel. Hence no solution are possible.

Hence, system is inconsistent for |a|=3

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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.