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

Answer

C

Explanation

`:' -1 le lt 0 :. [x] =-1`
`0le y lt 1 :. [y] =0`
`1 le z lt 2 :. [z] =1`
Hence the given determinant is
`|{:(0,,0,,1),(-1,,1,,1),(-1,,0,,2):}|=1-[z]`