A circuit contains three identical resistors with $R=9.0\Omega$, two identical inductors with $L=2.0\text{mH}$, and an ideal battery with $\epsilon =18\text{V}$. The current '$i$ ' through the battery just after the switch is closed is:

Just after the switch is closed ($t=0$), an inductor behaves as an infinite resistance (open circuit) because it opposes the sudden change in current.Looking at the circuit diagram (implied from the 2017 paper), the battery is connected to a branch with a resistor and another branch containing inductors. The branches with inductors will have zero current. Only the branch with the single resistor (not in series with an inductor) will draw current.
$$i=\frac{\epsilon }{R}=\frac{18}{9}=2\text{A}$$