CAT 2020

Slot 2

QA

Question & Solution

$x^{2}-2\mid x\mid+\mid a-2\mid=0$

where $x>= 0$ and $x>=2$

$x^2-2x+a-2\ =0$ Using quadratic equation we have $x=\ 1+\sqrt{\ 3-a}\ and\ x=1-\sqrt{\ 3-a}$ Only two integer values are possible

a=2 and a=3. So corresponding "x" values are $x=1$ and $a=3$, $x=2$ and $a=2$, $x=0$ and $a=2$

where $x>=0$ and $x<2$

Applying the above process we get $x=1$ and $a=1$

where $x<0$ and $x>=2$ we get $a=3$ and $x=-1$ , $a=2$ and $x=-2$

where $x<0$ and $x<2$ we get $a=1$ and $x=-1$

Hence there are total 7 values possible