JEE Main 2022MathematicsDeterminantsMediumMCQ

JEE Main 2022 — Determinants Question with Solution

JEE Main 2022 (29 Jul Shift 2)

Question

If the system of equations

x+y+z=6

2x+5y+αz=β

x+2y+3z=14

has infinitely many solutions, then α+β is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C44

Step-by-step explanation

x+y+z=6     ....1

2x+5y+αz=β   ....2

x+2y+3z=14     ...3

For infinite solution 

11125α123=0

⇒15-2α-6-α+4-5=0

⇒8-α=0⇒α=8

Also 11625β1214=0

⇒70-2β-28-β+64-5=0

⇒36-β=0

i.e. α=8, β=36

⇒α+β=44

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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.