If $\cos (x-y), \cos x, \cos (x+y)$ are three distinct numbers which are in harmonic progression and $\cos x \neq \cos y$,then $1+\cos y$ is equal to

The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringes from the centre is

The reduction potential of a hydrogen half-cell will be negative if:

$A$ capacitor of capacity $4 \mu F$ is charged to $80 \ V$ and another capacitor of capacity $6 \mu F$ is charged to $30 \ V$. When they are connected,the energy lost by the $4 \mu F$ capacitor is: (in $mJ$)

$A$ lead bullet at $27\,^{\circ}C$ 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 $= 327\,^{\circ}C$,specific heat of lead $= 0.03\,cal/g\,^{\circ}C$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

$A$ positively charged $(+q)$ particle of mass $m$ has kinetic energy $K$ and enters a region with a horizontal magnetic field of induction $\overrightarrow{B}$ in a vertically downward direction. The acceleration of the particle is: