JEE Main 2023MathematicsDeterminantsEasyMCQ

JEE Main 2023 — Determinants Question with Solution

JEE Main 2023 (01 Feb Shift 1)

Question

Let S denote the set of all real values of λ such that the system of equations

λx+y+z=1

x+λy+z=1

x+y+λz=1
is inconsistent, then ∑λ∈Sλ2+λ is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D6

Step-by-step explanation

System of equations 

λx+y+z=1x+λy+z=1x+y+λz=1

has no solution, so

λ111λ111λ=0

⇒λ+22+λ2+λ1λ111λ=0

⇒2+λ1111λ111λ=0

⇒2+λ1001λ-1010λ-1=0

⇒2+λλ-12=0

⇒λ=1, -2

For λ=1, we get infinite solutions, since equation will be identical.

So,

∑λ2+λ=4+2=6 

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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.