Let $R$ be a rectangle,$C$ be a circle,and $T$ be a triangle in the plane. The maximum possible number of points common to the perimeters of $R, C$ and $T$ is

If the circles $x^2+y^2=9$ and $x^2+y^2+2\alpha x+2y+1=0$ touch each other internally,then the value of $\alpha^3$ is

If the midpoint of the chord intercepted by the circle $x^2+y^2-8x+10y+5=0$ on the line $2x+y+2=0$ is $(h, k)$,then $k+4h=$

If $x^2 + y^2 + 2gx + 2fy + c = 0$ is the equation of the smallest circle passing through $(1, 2)$ and touching the line $x + y - 7 = 0$,then the value of $(g + 2f + 3c)$ is -

Let $A(2,3)$,$B(3,-1)$,and $C(-3,2)$ be three points. If the centre of the circle passing through $A$,$B$,and $C$ is $O(h, k)$,then find the value of $2k - 4h$.

Consider $L_1: 2x + 3y + p - 3 = 0$; $L_2: 2x + 3y + p + 3 = 0$,where $p$ is a real number,and $C: x^2 + y^2 + 6x - 10y + 30 = 0$.
$STATEMENT-1$: If line $L_1$ is a chord of circle $C$,then line $L_2$ is not always a diameter of circle $C$.
$STATEMENT-2$: If line $L_1$ is a diameter of circle $C$,then line $L_2$ is not a chord of circle $C$.