The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled, the new resultant vector becomes perpendicular to $\vec{A}$, then the magnitude of $\overrightarrow{\mathrm{C}}$ is

A convex lens of focal length $\frac{1}{3} \mathrm{~m}$ forms a real, inverted image twice the size of the object. The distance of the object from the lens is

The frequency of a tuning fork is 256 Hz . It will not resonate with the tuning fork of frequency

A particle carrying a charge equal to 1000 times the charge on an electron, is rotating one rotation per second in a circular path of radius ' $r$ ' $m$. If the magnetic field produced at the centre of the path is $x$ times the permeability of vacuum, the radius ' r ' in m is $\left[\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right]\left[\mathrm{x}=2 \times 10^{-16}\right]$