JEE Main 2014MathematicsDeterminantsMediumMCQ

JEE Main 2014 — Determinants Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If a, b, c  are non - zero real numbers and if the system of equations

a-1x=y+z

b-1y=x+z

c-1z=x+y

has a non - trivial solution, then ab+bc+ca  equals :

Choose an option

Show full solutionCorrect option: C
Correct answer
Cabc

Step-by-step explanation

Given, a-1x=y+z⇒a-1x-y-z=0

b-1y=z+x⇒-x+b-1y-z=0

c-1z=y+x=-x-y+c-1z=0

For a non-trivial solution

a-1-1-1-1b-1-1-1-1c-1=0

⇒   1-a1111-b1111-c=0

⇒   1-a1-b1-c-1-11-c-1+1-1-b=0

⇒   1-a+b+c+ab+bc+ca-abc-1+a+b+c=0

⇒ab+bc+ca=abc

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About this question

This is a previous-year question from JEE Main 2014, 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.