JEE Main 2020MathematicsDeterminantsMediumMCQ

JEE Main 2020 — Determinants Question with Solution

JEE Main 2020 (08 Jan Shift 1)

Question

For which of the following ordered pairs μ,δ, the system of linear equations
x+2y+3z=1
3x+4y+5z=μ
4x+4y+4z=δ
is inconsistent?

Choose an option

Show full solutionCorrect option: A
Correct answer
A4,3

Step-by-step explanation

D=345123444      R3→R3-2R1+3R2
    =345123000 =0
Now, let P3≡4x+4y+4z-δ=0. If the system has solutions it will have infinite solution, so,P3≡αP1+βP2
Hence, 3α+β=4 and 4α+2β=4⇒α=2 and  β=-2
So, for infinite solution 2μ-2=δ

For system to be inconsistent,

 2μ≠δ+2
So, checking option, (4, 3) satisfies.

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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.