A bulb and an iron core inductor are connected to an AC source through key as shown in figure :

The bulb glows with certain brightness. Now iron rod is taken out of the inductor. Then the brightness of bulb.

increases

When the iron rod is taken out , the magnetic field inside the solenoid is decreased. This decreases the inductance of the solenoid.So , the inductive reactance of the solenoid decreases hence the brightness increases.