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For the point (⌊ P+1⌋, ⌊ P⌋), where ⌊ x⌋ denotes the greatest integer less than or equal to x, suppose it lies strictly inside the annular region enclosed by the circles x²+y²-2x-15=0 and x²+y²-2x-7=0. Then which of the following is true?
- P ∈ [-1,0) ∪ [0,1) ∪ [1,2)
- P ∈ [-1,2)∖{0,1}
- P ∈ (-1,2)
- None of these
Correct answer: None of these
Solution
The point ((⌊ P+1⌋,⌊ P⌋) must lie strictly between the two circles defined by the equations, which restricts the possible values of P beyond the intervals provided in the other options. Therefore, none of the specified ranges accurately capture the valid values for P.
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