Tangent galvanometer measures

$A$ compass needle of an oscillation magnetometer oscillates $20$ times per minute at a place $P$ where the angle of dip is $30^{\circ}$. The number of oscillations per minute becomes $10$ at another place $Q$ where the angle of dip is $60^{\circ}$. The ratio of the total magnetic field at the two places $(B_{Q}: B_{P})$ is:

$A$ 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$)

The period of oscillations of a magnetic needle in a magnetic field is $1.0 \, s$. If the length of the needle is halved by cutting it,the time period will be.....$s$.

To compare magnetic moments of two magnets by vibration magnetometer,the 'sum and difference method' is better because:

$A$ neutral point is obtained at the centre of a vertical circular coil carrying current. The angle between the plane of the coil and the magnetic meridian is.......$^o$