If  [ ] denotes the greatest integer less than or equal to the real number under consideration and −1≤x<0,0≤y<1, 1≤z<2 then the value of the determinant [x]+1[y][z][x][y]+1[z][x][y][z]+1, is

# 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

1. A

$\left[z\right]$

2. B

[y]

3. C

$\left[x\right]$

4. D

none of these

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### Solution:

We have, [x] = -1, [y] = 0 and [z] = 1

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