Which of the following are not state functions?
(I) `q+w`
(II)`q`
(III) `w`
(IV) `H-TS`

Options

A. (I) and (IV)
B. (II), (III) and (IV)
C. (I), (II) and (III)
D. (II) and (III)

Answer

To determine which of the given options are not state functions, we need to understand the definitions of state functions and path functions.

### Step-by-Step Solution:

1. **Understanding State Functions**:
- State functions are properties that depend only on the current state of the system, regardless of how that state was reached. Examples include internal energy (U), enthalpy (H), entropy (S), and Gibbs free energy (G).

2. **Analyzing the Options**:
- **(I) `q + w`**: This expression represents the change in internal energy (ΔU) of a system, where `q` is the heat added to the system and `w` is the work done on the system. Since internal energy is a state function, `q + w` is also a state function.

- **(II) `q`**: Heat (q) is a path function because it depends on the specific process taken to transfer heat to or from the system. Therefore, `q` is not a state function.

- **(III) `w`**: Work (w) is also a path function, as it depends on the path taken to do work on or by the system. Thus, `w` is not a state function.

- **(IV) `H - TS`**: This expression is related to Gibbs free energy (G), which is a state function. Since Gibbs free energy is a thermodynamic property, `H - TS` is also a state function.

3. **Conclusion**:
- The options that are not state functions are (II) `q` and (III) `w`.

### Final Answer:
The options that are not state functions are: **(II) `q` and (III) `w`**.