A neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$, where $\mu_{0}$ and $c$ are the permeability and speed of light in free space, respectively. Then,
$x=1, y=2, z=4$ and $u=-3$
$x=1, y=2, z=4$ and $u=3$
$x=-1, y=2, z=4$ and $u=-3$
$x=-1, y=2, z=4$ and $u=3$
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are
In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is
In the relation $P = \frac{\alpha }{\beta }{e^{ - \frac{{\alpha Z}}{{k\theta }}}}$ $P$ is pressure, $Z$ is the distance, $k$ is Boltzmann constant and $\theta$ is the temperature. The dimensional formula of $\beta$ will be