The correct answer is B. Mutual inductance.
Mutual inductance is the ability of a changing current in one coil to induce a voltage in another coil. In an LVDT, two coils are wound around a ferromagnetic core. The primary coil is connected to an AC voltage source, and the secondary coil is connected to an amplifier. When the core is moved, the mutual inductance between the coils changes, which induces a voltage in the secondary coil. The amplitude of the voltage in the secondary coil is proportional to the displacement of the core.
Self inductance is the ability of a coil to store energy in its magnetic field. It is proportional to the square of the current flowing through the coil. Reluctance is the opposition to the flow of magnetic flux in a material. Permanence is the ability of a material to retain a magnetic field after the magnetizing force has been removed.
In an LVDT, the self inductance and reluctance of the coils are not important. The only factor that affects the output voltage is the mutual inductance between the coils.