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

Options

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

Explanation

To determine which of the given options are not state functions, we will analyze each option one by one.

### Step-by-Step Solution:

1. **Understanding State Functions**:
- State functions are properties that depend only on the state of the system, not on the path taken to reach that state. Examples include internal energy (U), enthalpy (H), and Gibbs free energy (G).

2. **Analyzing Option (I): `q + w`**:
- According to the first law of thermodynamics, \( q + w = \Delta U \), where \( \Delta U \) is the change in internal energy.
- Since internal energy (U) is a state function, \( q + w \) is also a state function.
- **Conclusion**: **State function**.

3. **Analyzing Option (II): `q`**:
- Heat (q) is a measure of energy transfer due to temperature difference and depends on the path taken during the process.
- Therefore, heat is a path function and not a state function.
- **Conclusion**: **Not a state function**.

4. **Analyzing Option (III): `w`**:
- Work (w) is also a measure of energy transfer and depends on the specific path taken during the process.
- Thus, work is a path function and not a state function.
- **Conclusion**: **Not a state function**.

5. **Analyzing Option (IV): `H - TS`**:
- The expression \( H - TS \) is related to the Gibbs free energy (G), which is defined as \( G = H - TS \).
- Gibbs free energy is a state function because it depends only on the state of the system (pressure, temperature, and composition).
- **Conclusion**: **State function**.

### Final Conclusion:
The options that are **not state functions** are:
- (II) `q`
- (III) `w`