If $y=y(x)$ is the solution of the differential equation, $\sqrt{4-x^2} \frac{\mathrm{~d} y}{\mathrm{~d} x}=\left(\left(\sin ^{-1}\left(\frac{x}{2}\right)\right)^2-y\right) \sin ^{-1}\left(\frac{x}{2}\right),-2 \leq x \leq 2, y(2)=\frac{\pi^2-8}{4}$, then $y^2(0)$ is equal to ___________.

The interior angles of a polygon with n sides, are in an A.P. with common difference 6°. If the largest interior angle of the polygon is 219°, then n is equal to _______.

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _______.

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is –3, then the magnitude of the radius of curvature of the mirror is :