Final answer:
Just after opening the switch S, the polarity of the induced emf in terminals X and Y is such that X is positive and Y is negative.
Step-by-step explanation:
When the switch S is opened, the current through the solenoid suddenly decreases, causing a decrease in magnetic flux through its coils.
According to Lenz's law, the induced emf in the solenoid will have a polarity that opposes the change causing it.
Therefore, the induced emf will have a polarity such that terminal X is positive and terminal Y is negative. This is represented by option B: X is positive and Y is negative.