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If [ ] represents the greatest integer less than or equal to the given real number, and -1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2, then the determinant [x] [y] [z] [x+1] [y+1] [z] [x] [y] [z]+1 is equal to:

1. [z]
2. [y]
3. [x]
4. None of these

Correct answer: None of these

Solution

The determinant involves the greatest integer function applied to variables constrained within specific ranges, leading to values that do not correspond directly to any of the options provided. The calculations reveal that the determinant does not simplify to any of the integers represented by [x], [y], or [z], confirming that 'None of these' is the correct answer.

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