Electric field at a point varies as $r^0$ for

The velocities of two particles $A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de-Broglie's wavelength is

$A$ lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^oC$,specific heat of lead $= 0.03\,cal/g\,^oC$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

$A$ current of $2\, A$ flows in a system of conductors as shown. The potential difference $(V_A - V_B)$ will be ................ $V$.

The value of $\cos^{-1}\left(\cos\frac{5\pi}{3}\right) + \sin^{-1}\left(\cos\frac{5\pi}{3}\right)$ is

$A$ man is watching two trains,one leaving and the other coming in with equal speeds of $4\, m/s$. If they sound their whistles,each of frequency $240\, Hz$,the number of beats heard by the man (velocity of sound in air $= 320\, m/s$) will be equal to