Old Nokia and other dumb phones had a great feature: the alarm would sound even when the phone was turned off. This meant you could go to bed knowing your phone wasn’t going to make a sound until it was time for the alarm to wake you. But what about modern iPhones? Will their alarms go off if Do Not Disturb is enabled?
Source : Will the Alarm Work if Your iPhone is Off, Silent, or Do Not Disturb?
