The correct answer is: 10.
The MACLS system is a train protection system that is used in India. It is designed to prevent train collisions by ensuring that trains only proceed when it is safe to do so. The system works by issuing a series of authorisations to the loco pilot, which allow the train to proceed to the next station.
If the home signal at the next station is extinguished, the loco pilot will be issued a 10-minute authorisation. This means that the train can proceed to the next station, but it must stop within 10 minutes of passing the extinguished signal. This ensures that the train does not collide with another train that may be approaching the station.
The other options are incorrect because they are not the correct authorisation that is issued to the loco pilot for an extinguished home signal in the MACLS system.