Q.

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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a

[x]

b

[y]

c

[z]

d

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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