A parallel-plate capacitor is disconnected from a battery, and the plates are pulled a small distance farther apart. Does Q increase, decrease, or stay the same?

Q stay the same

Explanation:

Charging of capacitor is done by battery. If battery is disconnected, charging will stop. There will not be any discharging as plates are separate. So pulling the plates apart will not affect the charge lying on the capacitor. It will decrease its capacity and increase its potential, keeping its charge constant.