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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[x]

[y]

[z]

none of these

answer is C.

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Detailed Solution

∵−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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