Question

If $S$ is the set containing values of $x$ satisfying $[x{]}^2-5[x]+6\le 0$, where $\left[x\right]$ denotes greatest integer function then $S$ contains :

• A. $(2,4)$
• B. $(2,4]$
• C. $[2,3]$
• D. $[2,4)$

Answer 1

The correct option is D $[2,4)$

GIF represents greatest integer function.
$\left[x\right]$ is an integer and is always less than or equal to $x.$
Now,
$[x{]}^2-5[x]+6\le 0$

$\Rightarrow \left(\right[x]-2)\left(\right[x]-3)\le 0$

$\Rightarrow \left[x\right]\in [2,3]$
$\therefore x\in [2,4)$
Hence, option D.