A

In the given matching problem, we analyze common thermodynamic properties.
1. **Adiabatic Bulk Modulus of a Gas**: The adiabatic bulk modulus is given as 𝑘 = γP, where γ is the heat capacity ratio. This corresponds to **[C]**.
2. **Slope of P-V Curve for Isothermal Process**: The slope of the isothermal process on a P-V curve is given by the negative of the ratio of pressure to volume, which equals -𝑃/𝑉. This corresponds to **[A]**.
3. **Degree of Freedom**: For monoatomic gases, the degree of freedom is given by f = 3N, where N is the number of moles. This corresponds to **[D]**.
4. **Ratio of Molar Heat Capacity at Constant Pressure to R**: For monoatomic ideal gases, this ratio equals γ. Therefore, it corresponds to **[B]**.
Based on this analysis, the correct matches are:
(i) matches with [C], (ii) matches with [A], (iii) matches with [D], and (iv) matches with [B].
This results in the answer: A.