Magnetic flux of $10 \mu Wb$ is linked with a coil,when a current of $2 \ mA$ flows through it. What is the self-inductance of the coil (in $mH$)?

An air-cored solenoid with length $30 \; cm$,area of cross-section $25 \; cm^{2}$ and number of turns $500$,carries a current of $2.5 \; A$. The current is suddenly switched off in a brief time of $10^{-3} \; s$. How much is the average back $emf$ induced (in $V$) across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.

$A$ branch of a circuit is shown in the figure. If the current is decreasing at the rate of $10^3 \ A \ s^{-1}$, then the potential difference between $A$ and $B$ is (in $V$)

What length of a very thin wire is required to obtain a solenoid of length $l_0$ and inductance $L$?

An average induced emf of $0.5 \,V$ appears in a coil when the current in it is changed from $10 \,A$ in one direction to $10 \,A$ in the opposite direction in $0.8 \,s$. The self-inductance of the coil is: (in $\,mH$)

Regarding self-inductance:
$A:$ The self-inductance of the coil depends on its geometry.
$B:$ Self-inductance does not depend on the permeability of the medium.
$C:$ Self-induced e.m.f. opposes any change in the current in a circuit.
$D:$ Self-inductance is the electromagnetic analogue of mass in mechanics.
$E:$ Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below: