JEE Main 2023MathematicsDeterminantsMediumMCQ

JEE Main 2023 — Determinants Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

Let α be a root of the equation a-cx2+b-ax+c-b=0 where a, b, c are distinct real numbers such that the matrix α2α1111abc is singular. Then the value of  a-c2b-ac-b+b-a2a-cc-b+c-b2a-cb-a is

 

Choose an option

Show full solutionCorrect option: B
Correct answer
B3

Step-by-step explanation

It is given that the matrix α2α1111abc is singular, so

α2α1111abc=0

⇒α2c-b-αc-a+b-a=0

Above equation holds true if α=1. Now, 

a-c2b-ac-b+b-a2a-cc-b+c-b2a-cb-a

=a-b3+b-c3+c-a3a-bb-cc-a

=3a-bb-cc-aa-bb-cc-a=3

∵x3+y3+z3=3xyz if x+y+z=0

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About this question

This is a previous-year question from JEE Main 2023, 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.