If the point $(1,4)$ lies inside the circle $x^2+y^2-6x-10y+p=0$ and the circle does not touch or intersect the coordinate axes,then

If the point $(2, \lambda)$ lies inside the circles $x^2+y^2=13$ and $x^2+y^2+x-2y=14$,then $\lambda$ lies in the set

If the tangent to the circle $x^2 + y^2 = r^2$ at the point $(a, b)$ meets the coordinate axes at the points $A$ and $B$,and $O$ is the origin,then the area of the triangle $OAB$ is

Given the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.

List-$I$	List-$II$
$A$. The equation of the polar of $(4, 3)$ with respect to $C$	$I$. $y+5=0$
$B$. The equation of the tangent at $(9, -5)$ on $C$	$II$. $x=1$
$C$. The equation of the normal at $(-7, -5)$ on $C$	$III$. $3x+8y=27$
$D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$	$IV$. $x=9$

Consider a pair of circles $(|x| - 1)^2 + y^2 = 1$. Ram is moving along the circle centered at $(1, 0)$ in the clockwise direction at a rate of $2 \ m/s$,and Shyam is moving along the circle centered at $(-1, 0)$ in the anticlockwise direction at a rate of $1 \ m/s$. If Ram and Shyam start their journey from the origin $(0, 0)$,then the rate of change of the distance between Ram and Shyam at the instant when Ram crosses the $x$-axis for the first time is:

The circle ${x^2} + {y^2} = 4$ cuts the line joining the points $A(1, 0)$ and $B(3, 4)$ in two points $P$ and $Q$. Let $\frac{BP}{PA} = \alpha$ and $\frac{BQ}{QA} = \beta$. Then $\alpha$ and $\beta$ are roots of the quadratic equation