Thank you for reporting, we will resolve it shortly
Q.
The current through a coil of self inductance $L = 2\,mH$ is given by $I = t^2\,e^{-t}$ at time $t$. How long it will take to make the e.m.f. zero ?
The current is given by the relation $i=t^{2} e^{-t}$.
Hence the emf would be equal to
$e=-L \frac{d i}{d t}=-2 \times 10^{-3} \times\left(2 t e^{-t}-t^{2} \,e^{-t}\right)$
If the emf is zero, $e=0$, hence
$2 t e^{-t}=t^{2}\, e^{-t} $
$\Rightarrow t=2\, s$