JEE Main 2021MathematicsDeterminantsMediumNumerical

JEE Main 2021 — Determinants Question with Solution

JEE Main 2021 (20 Jul Shift 1)

Question

Let a,b,c,d be in arithmetic progression with common difference λ. If x+a-cx+bx+ax-1x+cx+bx-b+dx+dx+c=2, then value of λ2 is equal to________.

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Correct answer
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Step-by-step explanation

Since, a, b, c & d are in A.P., therefore

b-a=c-b=d-c=λ

We have,

x+a-cx+bx+ax-1x+cx+bx-b+dx+dx+c=2

C2→C2-C3

⇒x-2λλx+ax-1λx+bx+2λλx+c=2

R2→R2-R1,  R3→R3-R1

x-2λλx+a2λ-10b-a4λ0c-a=2

⇒λx-2λ1x+a2λ-10λ4λ02λ=2

⇒-λ4λ2-4λ2-2λ=2

⇒λ2=1

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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.