JEE Main 2017MathematicsDeterminantsEasyMCQ

JEE Main 2017 — Determinants Question with Solution

JEE Main 2017 (08 Apr Online)

Question

The number of real values of λ for which the system of linear equations, 2x+4y-λz=0, 4x+λy+2z=0 and λx+2y+2z=0, has infinitely many solutions, is:

Choose an option

Show full solutionCorrect option: B
Correct answer
B1

Step-by-step explanation

For Infinite many solution Δ=0

i.e , 24-λ4λ2λ22=0 

⇒ 22-2λ-48-2λ-λ8-λ2=0

⇒λ3+4λ-40=0 

f(x)=x3+4x-40 is strictly increasing

i.e., equation has only one real root,

Also, ∆1=0, ∆2=0, ∆3=0

∴ Only one value of λ is possible

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About this question

This is a previous-year question from JEE Main 2017, 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.