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The point $([p + 1], [p])$ lying inside the circle $x^{2} + y^{2} - 2 x - 15 = 0,$ then set of all values of p is (where [.] represent greatest integer function)

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$(- 2, 3)$

$[- 2, 3)$

$[- 2, 0) \cup (0, 3)$

$[0, 3)$

answer is A.

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Detailed Solution

$\begin{array}{l} S_{11} < 0 \\ [p + 1]^{2} + [p]^{2} - 2 [p + 1] - 15 < 0, [x + k] = [x] + k \\ [p]^{2} < 8 - 2 \sqrt{2} < [p] < 2 \sqrt{2} \end{array}$

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