$A$ coil is wound on a core of rectangular cross-section. If all the linear dimensions of the core are increased by a factor of $2$ and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of (Assume, permeability is same).

The current in an inductor is given by $I = (3t + 8)$ $A$,where $t$ is in seconds. The magnitude of the induced emf produced in the inductor is $12 \ mV$. The self-inductance of the inductor is . . . . . . $mH$.

The average $e.m.f.$ induced in a coil in which the current changes from $2 \ A$ to $4 \ A$ in $0.05 \ s$ is $8 \ V.$ What is the self-inductance of the coil in $H$?

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.

Define inductance, give its units and write factors on which its value depends.

If in a coil the rate of change of area is $5 \, m^2/ms$ and the current changes from $2 \, A$ to $1 \, A$ in $2 \times 10^{-3} \, s$. If the magnetic field is $1 \, T$,then the self-inductance of the coil is......$H$