A small magnetised needle $P$ placed at point $O$ and the arrow shows the direction of its magnetic moment. The other arrow show different position (and orientation) of another identical magnets $(Q)$. In which configuration system is not in equilibrium

Two like magnetic poles of strength $ 10$  and $40$ $ SI$ units are separated by a distance $30 \,cm$. The intensity of magnetic field is zero on the line joining them

Below figures $(1)$ and $(2)$ represent lines of force. Which is correct statement

A short bar magnet with its north pole facing north forms a neutral point at $P$ in the horizontal plane. If the magnet is rotated by $90^o$ in the horizontal plane, the net magnetic induction at $P$ is (Horizontal component of earth’s magnetic field = ${B_H}$)

A bar magnet having centre $O$ has a length of $4 $ $cm. $ Point $P_1$ is in the broad side-on and $P_2 $ is in the end side-on position with $OP_1 = OP_2 = 10$ metres. The ratio of magnetic intensities $H$ at $P_1$ and $P_2$ is

The magnetic field due to a short magnet at a point on its axis at distance $X \,cm $ from the middle point of the magnet is $200 $ $Gauss$. The magnetic field at a point on the neutral axis at a distance $ X \,cm$  from the middle of the magnet is.....$Gauss$