The least distance of the point $\mathrm{A}(10,7)$ from the circle $x^2+y^2-4 x-2 y-20=0$ is length of seg AM . If $\mathrm{MM}^{\prime}$ is the diameter of the circle, then the lengths of AM and $\mathrm{AM}^{\prime}$ are respectively ___________ , ____________units

If the foot of the perpendicular drawn from the origin to a plane is $\mathrm{P}(-1,-1,2)$, then equation of the plane is

In a triangle $A B C$, with usual notations, if $a=5$, $\mathrm{b}=7 \sin \mathrm{~A}=\frac{3}{4}$, then total number of triangles possible are

If $\sin ^{-1}(4 x)+\sin ^{-1}(4 \sqrt{3} x)=-\frac{\pi}{2}$, then the value of $x$ is