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If [ ] denotes the greatest integer less than or equal to the real number under consideration and $-1 \leq x<0 ; 0 \leq y<1 ; 1 \leq z<2,$ then the value of the determinant
is
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is
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The correct answer is:
$[z]$
Since, $-1 \leq x<0$ $\begin{array}{ll}\therefore \quad & {[\mathrm{x}]=-1} \\ & 0 \leq \mathrm{y}<1 \quad \therefore[\mathrm{y}]=0 \\ & 1 \leq \mathrm{z}<2 \quad \therefore[\mathrm{z}]=1 \\ \therefore \quad & \text { Given determinant }=\left|\begin{array}{ccc}0 & 0 & 1 \\ -1 & 1 & 1 \\ -1 & 0 & 2\end{array}\right|=1=[\mathrm{z}]\end{array}$
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