An air core solenoid has $1000$ turns and is one metre long. Its cross-sectional area is $10 \, cm^2$. Its self-inductance is: (in $, mH$)

The inductance of a close-packed coil of $400$ turns is $8 \, mH$. $A$ current of $5 \, mA$ is passed through it. The magnetic flux through each turn of the coil is

The unit of self-inductance of a coil is

$A$ $10 \; \Omega, 20 \; mH$ coil carrying constant current is connected to a battery of $20 \; V$ through a switch. When the switch is opened, the current becomes zero in $100 \; \mu s$. The average emf induced in the coil is $\dots \; V$.

$A$ $12\,V$ battery connected to a coil of resistance $6\,\Omega$ through a switch,drives a constant current in the circuit. The switch is opened in $1\,ms$. The emf induced across the coil is $20\,V$. The inductance of the coil is ........... $mH$.

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1 :$ Self inductance of a long solenoid of length $L,$ total number of turns $N$ and radius $r$ is less than $\frac{{\pi {\mu _0}{N^2}{r^2}}}{L}$
Statement $2:$ The magnetic induction in the solenoid in Statement $1$ carrying current $I$ is $\frac{{{\mu _0}NI}}{L}$ in the middle of the solenoid but becomes less as we move towards its ends.