JEE Main 2020MathematicsDeterminantsMediumNumerical

JEE Main 2020 — Determinants Question with Solution

JEE Main 2020 (07 Jan Shift 2)

Question

If the system of linear equations,
x+y+z=6
x+2y+3z=10
3x+2y+λz=μ
has more than two solutions, then μ-λ2, is equal to.

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Show full solutionCorrect answer: 13
Correct answer
13

Step-by-step explanation

x+y+z=6  ...1
x+2y+3z=10  ...2
3x+2y+λz=μ  …3

From 1 & 2,
If z=0⇒x+y=6 and x+2y=10, ⇒y=4, x=2
If y=0⇒x+z=6 and x+3z=10, ⇒z=2, x=4

So, 3x+2y+λz=μ, must pass through (2,4,0) and (4,0,2).

6+8=μ⇒μ=14
And 12+2λ=μ ⇒λ=1

So, μ-λ2=14-1=13

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About this question

This is a previous-year question from JEE Main 2020, 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.