In an inductor of self-inductance $L = 2 \, mH$,current changes with time according to the relation $i = t^2 e^{-t}$. At what time is the $emf$ zero? (in seconds)

The length of a wire required to make a solenoid of length $l$ and self-induction $L$ is

$A$ coil and a bulb are connected in series with a $12 \,V$ direct current $(DC)$ source. $A$ soft iron core is now inserted into the coil. Then,

The $SI$ unit of inductance,the henry,cannot be written as:

The self-inductance of a long solenoid of cross-sectional area $A$,length $l$ and $n$ turns per unit length is given by

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.