JEE Main 2022MathematicsDeterminantsEasyMCQ

JEE Main 2022 — Determinants Question with Solution

JEE Main 2022 (24 Jun Shift 1)

Question

The number of values of α for which the system of equations
x+y+z=α

αx+2αy+3z=-1

x+3αy+5z=4

is inconsistent, is

Choose an option

Show full solutionCorrect option: B
Correct answer
B1

Step-by-step explanation

Given linear equations are 

x+y+z=α

αx+2αy+3z=-1

x+3αy+5z=4

For this system of linear equations to have inconsistent solution

D=111α2α313α5=0

⇒α-12=0

⇒α=1

Now for α=1

D1=111-123435

=10-9--5-12+-3-8

=1+17-11≠0

Hence, for α=1 the system of equation has inconsistent solution.

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About this question

This is a previous-year question from JEE Main 2022, 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.