**Explanation:**

The state of a system is defined by its properties or variables. In the case of a mixture of gases, the state of the system can be defined by a set of independent intrinsic variables.

**Intrinsic Variables:**
Intrinsic variables are properties that depend only on the state of the system and not on its history or how it got to that state. In the case of a gas mixture, the intrinsic variables are typically temperature, pressure, and composition.

**Temperature (T):**
Temperature is a measure of the average kinetic energy of the gas molecules. It determines the thermal state of the system.

**Pressure (P):**
Pressure is the force exerted by the gas molecules on the walls of the container. It determines the mechanical state of the system.

**Composition (i.e., mole fractions of the gases):**
The composition of the gas mixture refers to the relative amounts of each gas present in the container. It determines the chemical state of the system.

**Independent Intrinsic Variables:**
To completely define the state of the gas mixture, we need a set of independent intrinsic variables. This means that changing one variable should not affect the others.

In the case of a gas mixture, we need at least three independent intrinsic variables to completely define the system. This is because the ideal gas law equation (PV = nRT) has three variables: pressure (P), volume (V), and temperature (T). However, since we are considering a fixed volume container, the volume is constant and does not need to be specified.

So, in this specific case, to completely define the state of the gas mixture, we need two independent intrinsic variables: temperature (T) and composition (mole fractions of O2 and N2 gases).

Therefore, the correct answer is option 'D' - 3 independent intrinsic variables are required to completely define the state of the system.