The point is lying inside the circle

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The point ([λ+1],[λ])([\lambda + 1], [\lambda]) is lying inside the circle x2+y2−2x−15=0x^2 + y^2 - 2x - 15 = 0 . Then, the set of all values of λ\lambda is (where [⋅][\cdot] represents the greatest integer function) (1) [−2,3][-2, 3] (2) (−2,3)(-2, 3) (3) [−2,0)∪(0,3)[-2, 0) \cup (0, 3) (4) [0,3)[0, 3)

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