Question

If [ ] 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. [z]
• B. [y]
• C. [x]
• D. None of these

Answer 1

Answer: (A)

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