The correct options are
A at t =0; current through the source is 2E3R
B at t=∞ ; current through the source is 2E3R
at t =0; replace capacitors with short ckt and inductors open ckt and at t=∞, replace capacitor with open ckt and inductor with short ckt.
By doing that the circuit will be simplified which will result in a current of 2E3R at t = 0 and at t = ∞ both.