According to the Debye-Hückel-Onsager equation, $\Lambda_m = \Lambda^{\circ}_m - A\sqrt{c}$ . Statement A: This equation applies only to strong electrolytes, as weak electrolytes show a steep increase in molar conductivity with dilution, which cannot be represented by this linear equation. So, statement A is incorrect. Statement B: The constant $A$ depends on the nature of the solvent (dielectric constant, viscosity) and temperature. So, statement B is correct. Statements C & D: The value of $A$ also depends on the type of electrolyte, i.e., the charges on the cation and anion produced upon dissociation. $\text{BaCl}_2$ dissociates into $\text{Ba}^{2+}$ and $2\text{Cl}^-$, making it a 2-1 electrolyte. $\text{MgSO}_4$ dissociates into $\text{Mg}^{2+}$ and $\text{SO}_4^{2-}$, making it a 2-2 electrolyte. Thus, they have different values of $A$. However, $\text{Mg(OH)}_2$ dissociates into $\text{Mg}^{2+}$ and $2\text{OH}^-$, making it a 2-1 electrolyte just like $\text{BaCl}_2$. Therefore, they have the same value for constant $A$. Thus, statement C is incorrect and statement D is correct. Hence, only statements (B) and (D) are correct.