JEE Main 2024MathematicsDeterminantsEasyMCQ

JEE Main 2024 — Determinants Question with Solution

JEE Main 2024 (01 Feb Shift 2)

Question

Let the system of equations x+2y+3z=5,2x+3y+z=9,4x+3y+λz=μ have infinite number of solutions. Then λ+2μ is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B17

Step-by-step explanation

Given: x+2y+3z=5, 2x+3y+z=9 and 4x+3y+λz=μ.

For infinite solutions, Δ=Δ1=Δ2=Δ3=0.

⇒Δ=12323143λ=0

⇒3λ-3-4λ+8+18-36=0

⇒λ=−13

Now, finding 

⇒Δ1=523931μ3−13=0

⇒μ=15

Now, finding

⇒Δ2=1532914μλ

⇒Δ2=153291415−13

⇒Δ2=0

And 

⇒Δ3=12523943μ

⇒Δ3=1252394315

⇒Δ3=0

For λ=−13, μ=15 system of equation has infinite solutions.

⇒λ+2μ=17.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Determinants chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2024, 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.