Two magnets are placed with their like poles together,and they perform $12$ oscillations in $1$ minute. When they are placed with their unlike poles together,they perform $4$ oscillations in $1$ minute. What is the ratio of the magnetic moments of the magnets?

$A$ bar magnet of length $14 \, cm$ is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. $A$ neutral point is obtained at a distance of $18 \, cm$ from the center of the magnet. If $B_{H} = 0.4 \, G$,the magnetic moment of the magnet is $\left(1 \, G = 10^{-4} \, T\right)$.

$A$ magnet of magnetic moment $M$ oscillating freely in earth's horizontal magnetic field makes $n$ oscillations per minute. If the magnetic moment is quadrupled and the earth's field is doubled,the number of oscillations made per minute would be

$A$ bar magnet of length $10 \, cm$ is kept with its north $(N)$-pole pointing north. $A$ neutral point is formed at a distance of $15 \, cm$ from each pole. Given the horizontal component of the earth's magnetic field is $0.4 \, Gauss$, the pole strength of the magnet is: (in $ \, A-m$)

Two magnets of same size and mass make respectively $10$ and $15$ oscillations per minute at a certain place. The ratio of their magnetic moments is

$A$ compass needle oscillates $20$ times per minute at a place where the dip is $45^{\circ}$ and the magnetic field is $B_1$. The same needle oscillates $30$ times per minute at a place where the dip is $30^{\circ}$ and magnetic field is $B_2$. Then $B_1: B_2$ is