JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q65

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MathematicsSingle correct+4 / -1Question 65 of 90

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 :

an infinite set

a finite set containing two or more elements

a singleton

an empty set

Answer and worked solution

Official answer: C

Subtracting the first equation from the second: $(a-1)y=0$ .

If $a\ne1$ , then $y=0$ , $x+z=1$ and $ax+z=0$ , which is always solvable.
If $a=1$ , the third equation is $x+by+z=0$ . Against $x+y+z=1$ it is inconsistent exactly when $b=1$ .

So $S=\{1\}$ , a singleton.

Topics:Systems of linear equations

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 65