JEE Main 2017MathematicsDeterminantsEasyMCQ

JEE Main 2017 — Determinants Question with Solution

JEE Main 2017 (09 Apr Online)

Question

If x=a, y=b, z=c is a solution of the system of linear equations
x+8y+7z=0
9x+2y+3z=0
x+y+z=0
Such that the point a,b,c  lies on the plane x+2y+z=6 , then 2a+b+c equals:

Choose an option

Show full solutionCorrect option: C
Correct answer
C1

Step-by-step explanation

x+8y+7z=0  ...i        9x+2y+3z=0  ...ii        x+y+z=0  ...iii             .....

Solve the equation i &iii

 ⇒7y+6z=0

Solve the equation ii &iii

⇒7x+z=0

x=λ & y=-6-7λ7 & z=-7λ

x=λ& y=6λ& z=-7λ

  ⇒λ+12λ−7λ=6⇒6λ=6⇒λ=1 | ⇒2λ+6λ−7λ⇒λ=1

Hence, a=1, b=6, c=-7

∴2a+b+c=1

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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.