Vector $\vec{A}$ of magnitude $5 \sqrt{3}$ units, another vector $\vec{B}$ of magnitude of 10 units are inclined to each other at an angle of $30^{\circ}$. The magnitude of vector product of the two vectors is $\left[\sin 30^{\circ}=\frac{1}{2}\right]$

The magnetic field intensity H at the centre of a long solenoid having $n$ turns per unit length and carrying a current I, when no material is kept in it is ( $\mu_0=$ permeability of free space)

Four particles each of mass M are placed at the corners of a square of side L . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

In Fraunhofer diffraction pattern, slit width is 0.3 mm and screen is at 1.5 m away from the lens. If wavelength of light used is $4500 \mathop {\rm{A}}\limits^{\rm{o}}$, then the distance between the first minimum on either side of the central maximum is [ $\theta$ is small and measured in radian.]