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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 $|\begin{array}{ccc} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{array}|$ is

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Correct option is C

∵−1≤x<0 ∴[x]=−10≤y<1 ∴[y]=01≤z<2 ∴[z]=1Hence, the given determinant is 001−111−102=1=[z]

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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

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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 $|\begin{array}{ccc} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{array}|$ is