JEE Main 2017MathematicsDeterminantsEasyMCQ

JEE Main 2017 — Determinants Question with Solution

JEE Main 2017 (02 Apr)

Question

If S is the set of distinct values of b for which the following system of linear equations

x+y+z=1

x+ay+z=1

ax+by+z=0

has no solution, then S  is:

Choose an option

Show full solutionCorrect option: D
Correct answer
DA singleton

Step-by-step explanation

For no solution D=1111a1ab1=0

Expanding the determinant along the first row, we get D=-a-12=0

⇒   a=1

For a=1, first two planes are coincident.

Now, we have x+y+z=1 & ax+by+z=0

For no solution, these two planes are parallel.

⇒1a=1b=11

⇒a=1 & b=1.

∴   b=1 ⇒ it is a singleton set

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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.