Question

If $\left[\right]$ denotes the greatest integer less than or equal to the real number under consideration and $-1\le x<0;0\le y<1;1\le z<2$, then the value of the determinant $\left[\begin{array}{ccc}\left[x\right]+1& \left[y\right]& \left[z\right]\\ \left[x\right]& \left[y\right]+1& \left[z\right]\\ \left[x\right]& \left[y\right]& \left[z\right]+1\end{array}\right]$ is

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

Answer 1

Answer: (A)

$\left[z\right]$

Since, $-1\le x<0$
$\therefore \left[x\right]=-1$
$0\le y\le 1\therefore \left[y\right]=0$
$1\le z<2\therefore \left[z\right]=1$
$\therefore$ Given determinant $=\left|\begin{array}{ccc}0& 0& 1\\ -1& 1& 1\\ -1& 0& 2\end{array}\right|=1=\left[z\right]$.