Mathematics - Area Under Curves Question with Solution | TestHub

$[P+1]=\left[P\right]+1$, Let $\left[P\right]=n$, then $n$ is integer

$\therefore \left(\right[P+1],[P\left]\right)=(n+1,n)$ lie inside the region of circles

$S_1=x^2+y^2-2x-15=0,C_1=(1,0),r_1=4$

and $S_2=x^2+y^2-2x-7=0,C_2=(1,0),r_2=2\sqrt{2}$

Both circles are concentric. 

$\therefore (n+1{)}^2+n^2-2(n+1)-7>0$

and $(n+1{)}^2+n^2-2(n+1)-15<0\Rightarrow 4<n^2<8$

Which is not possible for any integer.