JEE Main 2022MathematicsDeterminantsEasyMCQ

JEE Main 2022 — Determinants Question with Solution

JEE Main 2022 (26 Jul Shift 1)

Question

If the system of linear equations.

8x+y+4z=-2

x+y+z=0

λx-3y=μ

has infinitely many solutions, then the distance of the point λ,μ,-12 from the plane 8x+y+4z+2=0 is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D103

Step-by-step explanation

Given the system of linear equations.

8x+y+4z=-2

x+y+z=0

λx-3y=μ

has infinitely many solutions, so

D=814111λ-30=0⇒λ=4

Also D1=D2=D3=0

D1=-214011μ-30=0⇒-6-3μ=0

So μ=-2

Hence the point will be 4,-2,-12

Now distance of point 4,-2,-12 from plane 8x+y+4z+2=0

=32-2-2+282+12+42=309=103

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About this question

This is a previous-year question from JEE Main 2022, 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.