For a reaction $\mathrm{A}\left(\mathrm{s}\right)\rightleftharpoons \mathrm{B}\left(\mathrm{s}\right)+\mathrm{C}\left(\mathrm{g}\right)$ the set of all correct statements are

a) $\mathrm{K}$ is independent of $\left[\mathrm{A}\right]$.

b) $\mathrm{K}$ is dependent on partial pressure of $\mathrm{C}$ at a given temperature.

c) $\mathrm{\Delta H}$ will be independent of temperature.

d) $\mathrm{\Delta H}$ is independent of the catalyst addition.

Given reaction is 

$\mathrm{A}\left(\mathrm{s}\right)\rightleftharpoons \mathrm{B}\left(\mathrm{s}\right)+\mathrm{C}\left(\mathrm{g}\right)$

Equilibrium constant for this reaction ${\mathrm{K}}_{\mathrm{C}} = \left[\mathrm{C}\right]$ concentration of solid is considered as one during heterogenous equilibrium. So, as we can see $\mathrm{K}$ is independent of $\left[\mathrm{A}\right]$.

Similarly ${\mathrm{K}}_{\mathrm{P}} = {\mathrm{P}}_{\mathrm{C}}$ So, $\mathrm{K}$ is dependent on partial pressure of $\mathrm{C}$.

Note: Although the value of equilibrium constant does not depend on concentration of reactants or products at a given temperature.

Enthalpy change depends on temperature, but it is independent of catalyst used.

So, statement a,b and d are correct.