For a ferromagnetic material,the relative permeability $(\mu_r)$ versus magnetic intensity $(H)$ has the following shape:

$(a)$ What happens if a bar magnet is cut into two pieces: $(i)$ transverse to its length,$(ii)$ along its length?
$(b)$ $A$ magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet,however,experiences a force of attraction in addition to a torque. Why?
$(c)$ Must every magnetic configuration have a north pole and a south pole? What about the field due to a toroid?
$(d)$ Two identical-looking iron bars $A$ and $B$ are given,one of which is definitely known to be magnetised. (We do not know which one.) How would one ascertain whether or not both are magnetised? If only one is magnetised,how does one ascertain which one? [Use nothing else but the bars $A$ and $B$.]

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Magnetic induction	$(I)$ Ampere meter$^2$
$(B)$ Magnetic intensity	$(II)$ Weber
$(C)$ Magnetic flux	$(III)$ Gauss
$(D)$ Magnetic moment	$(IV)$ Ampere meter

Choose the correct answer from the options given below:

$A$ bar magnet has a total length $2l = 20$ units and the field point $P$ is at a distance $d = 10$ units from the centre of the magnet. If the relative uncertainty of length measurement is $1\%$,then the uncertainty of the magnetic field at point $P$ is

Two short magnets of magnetic moment $1000 \, A m^2$ are placed as shown at the corners of a square of side $10 \, cm$. The net magnetic induction at $P$ is....$T$

Magnetostatic screening or shielding can be created by