### JEE Main Solved Paper 2017 Question 5

##### 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 : [JEE Main Solved Paper-2017]

#### Options:

A) a singleton

B) an empty set

C) an infinite set

D) a finite set containing two or more elements

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

$ D= \begin{matrix} 1 & 1 & 1 \\ 1 & a & 1 \\ a & b & 1 \\ \end{matrix} =0\Rightarrow a=1 $ and at $ a=1 $ $ D _1=D _2=D _3=0 $
$ \begin{matrix} First two equations are \\ and third equation is \\ \end{matrix}. \begin{matrix} x+y+z=1 \\ x+y+z=0 \\ \end{matrix} \Rightarrow There is no solution $

$ \therefore $ $ b={1}\Rightarrow $ it is a singleton set