Refer to figures.
EASA learning objective 022.05.02.01.07 states: 'Explain that, on a modern aircraft, there is likely to be an air-data inertial reference unit (ADIRU), which is an inertial reference unit (IRU) integrated with an air-data computer (ADC).'

An air data computer (ADC) acts as a central processing point for all the aircraft instruments and systems that need air data parameters in a digital format. Total pressure, static pressure, temperature and angle of attack are input from their respective probes and the ADC performs the necessary calculations to output such parameters as TAS, CAS, altitude and SAT in a digital format that can be processed by the aircrafts systems that require it.

Modern aircraft combine the ADC and Inertial Reference Unit (IRU) into a one box unit known as an air-data inertial reference unit (ADIRU). For redundancy an aircraft will have 2 or 3 ADIRU's which make up an air data inertial reference system (ADIRS). This sensor fusion of air and inertial data is far more efficient than having separate systems.

The air data and inertial reference parts of the system can function independently if required following the failure of one part of the system. Separate controls are supplied on the ADIRS control panel (see figure).

ADIRU is an Air Data Computer which is integrated with an Inertial Reference Unit --> CORRECT. As stated in LO 022.05.02.01.07

ADIRU is an Air Data Computer which is integrated with an Inertial Unit and GPS --> INCORRECT. An ADIRU does not have a GNSS integrated into it.

ADIRU is an Attitude Director Indicator which is integrated with an Inertial Reference Unit --> INCORRECT. An attude director indicator is a flight instrument on the pilots instrument panel, it is not integrated into an ADIRU.

ADIRU is an Air Data Computer which is integrated with an Inertial Navigation System --> Inertial Navigation Systems pre date IRS and are stand alone navigation systems.