The equation of a plane progressive wave is given by $y = 5 \cos \pi \left( 200t - \frac{x}{150} \right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ________ m/s.

Two short electric dipoles A and B having dipole moment $p_1$ and $p_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ is making an angle of $60^{\circ}$ with the line joining points $O$ and $x$. The ratio of the dipole moments $p_2/p_1$ is _________.

For the given circuit (shown in part (A)) the time dependent input voltage $v_{in}(t)$ and corresponding output $v_{o}(t)$ are shown in part (B) and part (C), respectively. Identify the components that are used in the circuit between points X and Y.

When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$. The number of turns, area of the coil and radius of the coil wire are $N$, $A$ and $r$ respectively. For a second coil number of turns, area of the coil and radius of the coil wire are $2N$, $2A$ and $3r$ respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt{2} \,\alpha P$. The value of $\alpha$ is ______.