Let's analyze each statement:

$$\textbf{A. The self-inductance of the coil depends on its geometry.}$$

This is true because the self-inductance of a coil is given by formulas that include its geometrical parameters (number of turns, cross-sectional area, length, etc.). For example, for a solenoid,

$$ L = \mu_0 \mu_r \frac{N^2 A}{l}, $$

where $$N$$ is the number of turns, $$A$$ is the cross-sectional area, and $$l$$ is the length.

$$\textbf{B. Self-inductance does not depend on the permeability of the medium.}$$

This is false. The permeability of the medium (represented by $$\mu = \mu_0 \mu_r$$) directly influences the inductance, as seen in the formula above. So, any change in the medium’s permeability will affect the inductance.

$$\textbf{C. Self-induced e.m.f. opposes any change in the current in a circuit.}$$

This is true, and it is a direct consequence of Lenz's law. The induced electromotive force (e.m.f.) always acts in a direction such that it opposes the change in current that produced it.

$$\textbf{D. Self-inductance is the electromagnetic analogue of mass in mechanics.}$$

This is true. Just as mass resists changes in velocity (inertia), inductance resists changes in current, which is why it is often compared to the inertial mass in mechanical systems.

$$\textbf{E. Work needs to be done against self-induced e.m.f. in establishing the current.}$$

This is true because, when you try to change the current, you must do work to overcome the opposing self-induced e.m.f., storing energy in the magnetic field of the inductor.

Based on the above reasoning, the true statements are A, C, D, and E.

Thus, the correct answer is:

Option C

A, C, D, E only