a bulb connected in series with a solenoid is lit by ac source. If a soft iron core is inroduced in the solenoid ,will the bulb glow brighter?

Inductors do not irreversibly consume energy. On average they neither consume nor generate energy. Therefore the bulb glows with the same brightness.

On inserting a soft iron core inside a solenoid(or inductor) the intensity of magnetic field increases and due to ac supply, change in magnetic flux increases and according to Faraday`s Second Law Of EMI the opposing emf will increase due to which the glow of the bulb decreases.

As above said due to induced emf the brightness decreases but if we let it stay for some more time it will regain its original brightness because inductor get nullified which is said in the first statement