Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-inductance is electromagnetic analogue of mass in mechanics.
E. Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

Let us analyze each statement about self-inductance:

Statement A: The self-inductance of a coil depends on its geometry (shape, size, number of turns). This is correct. For example, for a solenoid, $$L = \mu_0 n^2 A l$$.

Statement B: Self-inductance does not depend on the permeability of the medium. This is incorrect. Self-inductance is directly proportional to the permeability. For a solenoid with a core, $$L = \mu n^2 A l$$, where $$\mu = \mu_0 \mu_r$$.

Statement C: Self-induced e.m.f. opposes any change in the current in a circuit. This is correct (Lenz's law). The self-induced emf is $$\varepsilon = -L\frac{dI}{dt}$$.

Statement D: Self-inductance is the electromagnetic analogue of mass in mechanics. This is correct. In the energy analogy, $$\frac{1}{2}LI^2$$ (electromagnetic) corresponds to $$\frac{1}{2}mv^2$$ (mechanical), so $$L$$ is analogous to mass $$m$$.

Statement E: Work needs to be done against self-induced e.m.f. in establishing the current. This is correct. The energy stored in the inductor $$\frac{1}{2}LI^2$$ is the work done against the self-induced emf.

Statements A, C, D, E are correct.

The correct answer is Option 3: A, C, D, E only.