Question

The point ([P + 1], [P]) lies in the region bounded by curves $x^2+y^2-2x-15=0$ and $x^2+y^2-2x-7=0$, {[∙] denotes greatest integer function} then

• A. $pϵ[-1,0)\cup (0,1)\cup (1,2)$
• B. $4<[p{]}^2<8$
• C. $pϵ(-2,2)-\{0,1\}$
• D. $0<[p{]}^2<4$

Answer 1

The correct option is B

$4<[p{]}^2<8$

$\left(\right[P+1],[P\left]\right)$ lies inside the circle $x^2+y^2-2x-15=0$

$\therefore [P+1{]}^2+[P{]}^2-2[P+1]-15<0$

$\Rightarrow [P{]}^2<8\dots (1)$

$\left(\right[P+1],[P\left]\right)$ lies outside the circle $x^2+y^2-2x-7=0$

$\therefore [P+1{]}^2+[P{]}^2-2[P+1]-7>0$

$\Rightarrow [P{]}^2>4\dots (2)$

$\therefore$ (1) & (2)

$\Rightarrow 4<[P{]}^2<8$