a) As given in the question a coil of resistance $$ R $$ and inductance $$ L $$ connected in parallel to a resistor $$ R $$ and in turn the combination connected to a battery. So the bulb which is connected with the arm of resistor $$R$$  lights up earlier because the induced emf generated by the coil opposes the current which produced it. it takes time for bulb in the$$r$$ of inductor to light up. b)  Both bulbs will h up with same brightness because an inductor does not offer resistance in the pat of $$D. C$$ current. Inductor only produces induced emf at the time of make or break circuit.