JEE Main 2015MathematicsDeterminantsMediumMCQ

JEE Main 2015 — Determinants Question with Solution

JEE Main 2015 (10 Apr Online)

Question

The least value of the product xyz (such that x,y and z are positive real numbers) for which the determinant x11    1y1  11z is non-negative is

Choose an option

Show full solutionCorrect option: C
Correct answer
C-8

Step-by-step explanation

Since  A.M ≥G.M

x+y+z3 ≥xyz13

x+y+z ≥3xyz13

Now, x11 1y1 11z=xyz-x+y+z+2

Now determinant is non-negative

⇒xyz-x+y+z+2≥0

⇒xyz-3xyz13+2 ≥0

Let xyz=t3

So, t3-3t+2 ≥0

⇒t+2(t2-2t+1)≥0⇒t+2(t-1)2≥0

⇒t≥-2

⇒t3≥-8

⇒ Least value of xyz= -8

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About this question

This is a previous-year question from JEE Main 2015, 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.