A regular polygon of 6 sides is formed by bending a wire of length $4 \pi$ meter.

If an electric current of $4 \pi \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7} \mathrm{~T}$.

The value of $x$ is _________.

The distance between object and its 3 times magnified virtual image as produced by a convex lens is $20 \mathrm{~cm}$. The focal length of the lens used is __________ $\mathrm{cm}$.

Three identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is ___________ .

A tuning fork resonates with a sonometer wire of length $1 \mathrm{~m}$ stretched with a tension of $6 \mathrm{~N}$. When the tension in the wire is changed to $54 \mathrm{~N}$, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ $\mathrm{Hz}$.