If `[]` denotes the greatest integer less than or equal to the ral number under consideration, and `-1lt=x<0,0lt=y<1,1lt=a<2,` then the value of the determinant `|[x]+1[y][z][x][y]+1[z][x][y][z]+1|` is `[x]` b. `[y]` c. `[z]` d. none of these

Options

A. `[x]`
B. `[y]`
C. `[z]`
D. none of these

Explanation

To solve the given problem, we need to evaluate the determinant:

\[
D = \begin{vmatrix}
[\text{x}] + 1 & [\text{y}] & [\text{z}] \\
[\text{x}] & [\text{y}] + 1 & [\text{z}] \\
[\text{x}] & [\text{y}] & [\text{z}] + 1
\end{vmatrix}
...