QJEEM21Ma943f: JEE Main 2021 Mathematics - Class 11 JEEM21Ma943f Solution: Let [ x ] denote the greatest integer x, where x R. If the…

For domain,

${{{\left| {[x]} \right| - 2} \over {\left| {[x]} \right| - 3}}}$ $\ge$ 0

Case I :

When ${\left| {[x]} \right| - 2}$ $\ge$ 0

and ${\left| {[x]} \right| - 3}$ > 0

$\therefore$ x $\in$ ( $-$ $\infty$ , $-$ 3) $\cup$ [4, $\infty$ ) ...... (1)

Case II :

When ${\left| {[x]} \right| - 2}$ $\le$ 0

and ${\left| {[x]} \right| - 3}$ < 0

$\therefore$ x $\in$ [ $-$ 2, 3) ..... (2)

So, from (1) and (2) we get

Domain of function

= ( $-$ $\infty$ , $-$ 3) $\cup$ [ $-$ 2, 3) $\cup$ [4, $\infty$ )

$\therefore$ (a + b + c) = $-$ 3 + ( $-$ 2) + 3 = $-$ 2 (a < b < c)

$\Rightarrow$ Option (3) is correct.