figure shows an arrangement by which current flows through the bulb is connected with coil bi when AC is passed through coilA

Dear Student
The answer to your question is as follows
a) Bulb X lights due to electromagnetic induction produced by coil A.
b) Due to decrease in the effect of coil A on the coil B. OR decrease in the electromagnetic induction produced by coil A.
c) As the sheet is inserted, the magnetic field inside the coil magnetizes the sheet of copper increasing the magnetic field inside it.Hence the inductance of the coil increases.Consequently, the inductive reactance of the coil increases.As a result a larger fraction of the applied AC  voltage appears across the inductor, leaving less voltage across the bulb.Therefore, the brightness of the bulb decreases.

Regards.

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