Question

If [a] denotes the greatest integer less than or equal to a and $-1\le x<0,0\le y<1,1\le z<2$, then $\left|\begin{array}{ccc}\left[x\right]+1& \left[y\right]& \left[z\right]\\ \left[x\right]& \left[y\right]+1& \left[z\right]\\ \left[x\right]& \left[y\right]& \left[z\right]+1\end{array}\right|$ is equal to

• A. $\left[x\right]$
• B. $\left[y\right]$
• C. $\left[z\right]$
• D. None of these

Answer 1

The correct option is C $\left[z\right]$

$-1\le x<0\to \left[x\right]=-1$

$0\le y<1\to \left[y\right]=0$

$1\le z<2\to \left[z\right]=1$

$\left|\begin{array}{ccc}0& 0& 1\\ -1& 1& 1\\ -1& 0& 2\end{array}\right|$

$=1=\left[z\right]$