JEE Main 2021MathematicsDeterminantsMediumMCQ

JEE Main 2021 — Determinants Question with Solution

JEE Main 2021 (31 Aug Shift 1)

Question

If the following system of linear equations
2x+y+z=5
x-y+z=3
x+y+a z=b
has no solution, then :

Choose an option

Show full solutionCorrect option: D
Correct answer
Da=13,b≠73

Step-by-step explanation

Given system of equations

2x+y+z=5
x-y+z=3
x+y+a z=b
has no solution, 

D=2111-1111a=0⇒-2a-2-a+1+2=0⇒a=13

D1=5113-11b1a=5-a-1 + -13a-b +13+b = -8a+2b-2

D2=2511311ba=23a-b -5 a-1+1b-3 = a-b+3

D3=2151-1311b=2-b-3 - 1 b-3 + 52 = 7-3b

For the system to have no solution ⇒D = 0 , D3 ≠ 0

∴ a = 13 , b ≠73.

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About this question

This is a previous-year question from JEE Main 2021, 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.