Question

The area (in sq. units) bounded by $\left[\left|x\right|\right]+\left[\left|y\right|\right]=2$ in the first and third quadrant is (where, $\left[.\right]$ is the greatest integer function),

• A. $4$
• B. $3$
• C. $6$
• D. $10$

Answer 1

Answer: (C)

$\left[x\right]+\left[y\right]=2$ (Let $x,y\ge 0$ )
$[x]+[y]=2$ (Let $x,y\ge 0)$
$\Rightarrow [x],[y]=2,0$ or 1,1 or 0,2
If $[x]=2$ and $[y]=0$ $\Rightarrow x\in [2,3)$ and $y\in [0,1)$ and so on Since, the curve is symmetric in the $I^{st}$ and $II{I}^{rd}$ quadrant
Hence, the required area $=6(1\times 1)=6$ sq. units