Dielectric strength of a dielectric material depends on which of the following?
$(a)$ The electrode with which the electric field is applied
$(b)$ The respective geometries of the dielectric
$(c)$ The electric field which is applied
$(d)$ All of these

Hint: In this question use the basics of the dielectric strength, it is defined as the maximum amount of voltage that can be applied to a substance such that it undergoes a dielectric breakdown, so resistance is directly related to the material’s dielectric strength. This will help get the right answer.

Complete step-by-step answer:
A material's dielectric strength is one measure of an insulator's electrical resistance.
This is defined as the maximum voltage per unit thickness needed to produce a dielectric breakdown through the material and is expressed in terms of Volts.
I.e. for a pure electrically insulating material, the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and becoming electrically conductive (i.e. without failure of its insulating properties).
Resistivity of a material is the resistance that a material presents to the flow of electrical charge.

Dielectric resistance is the voltage that an insulating material can tolerate before a breakdown takes place. It typically depends on the thickness of the material and on the test method and conditions, i.e. in an electrical material, if the thickness of the material increases the breakdown voltage and thus the dielectric strength is also increased.

Now as we know that with the change of temperature the movement of electrons in a material changes and hence it affects the breakdown voltage of the material.
The electric field has a direct relation to the voltage breakdown or dielectric power. An increase in the electric field can contribute to increased dielectric force.

A perfect vacuum has the highest dielectric strength, rated at $1 \times {10^{12}}$ MV/m.
So all of the given options affect dielectric strength.
So this is the required answer.

Hence option (D) none of these is the correct answer.

Note: Dielectric materials are those that are loosely bound so when these materials are placed in an electric field no current flows through it, thus they can be considered as high insulating materials that are very poor conductors of electricity. Earth itself is a dielectric with 0 conductivity and finite dielectric constant.