A) \[P\in [-1,0)\cup [0,1)\cup [1,2)\]
B) \[P\in [-1,\,\,2)-\{0,\,\,1\}\]
C) \[P\in (-1,\,\,2)\]
D) None of these
Correct Answer: D
Solution :
[d] Since the \[([P+1],[P])\] lies inside the circle \[{{x}^{2}}+{{y}^{2}}-2x-15=0\] \[[But[x+n]=[x]+n,n\in N]\] \[\therefore \,\,\,\,\,{{[P+1]}^{2}}+{{[P]}^{2}}-2[P+1]-15<0\] \[{{([P]+1)}^{2}}+{{[P]}^{2}}-2([P]+1)-15<0\] \[2{{[P]}^{2}}-16<0,\,\,\,{{[P]}^{2}}<8\] ?. (1) From the second circle \[{{([P]+1)}^{2}}+{{[P]}^{2}}=-2([P]+1)-7>0\] \[\Rightarrow 2{{[P]}^{2}}-8>0,{{[P]}^{2}}>4\] ?. (2) From (1) & (2), \[4<{{[P]}^{2}}<8,\] which is not possible \[\therefore \] For no values of ?P? the point will be within the region.
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