To determine which set of quantities cannot enter into the list of fundamental quantities in any system of units, we need to analyze each option based on the definitions of fundamental quantities. Fundamental quantities are those that are independent of other quantities and cannot be derived from them.
### Step-by-Step Solution:
1. **Understanding Fundamental Quantities**:
- Fundamental quantities are independent and cannot be expressed in terms of other quantities. Common examples are length, mass, and time.
2. **Evaluate Option A: Length, Mass, and Velocity**:
- Length (L) is a fundamental quantity.
- Mass (M) is a fundamental quantity.
- Velocity (V) is defined as \( V = \frac{L}{T} \) (length per unit time), meaning it depends on length and time.
- Since velocity is derived from length and time, this set cannot be considered fundamental.
3. **Evaluate Option B: Length, Time, and Velocity**:
- Length (L) is a fundamental quantity.
- Time (T) is a fundamental quantity.
- Velocity (V) is defined as \( V = \frac{L}{T} \), which means it is derived from length and time.
- However, since both length and time are fundamental, this set is valid.
4. **Evaluate Option C: Mass, Time, and Velocity**:
- Mass (M) is a fundamental quantity.
- Time (T) is a fundamental quantity.
- Velocity (V) is defined as \( V = \frac{L}{T} \), which means it depends on length and time, but not on mass.
- Therefore, this set cannot be considered fundamental.
5. **Evaluate Option D: Length, Time, and Mass**:
- Length (L) is a fundamental quantity.
- Time (T) is a fundamental quantity.
- Mass (M) is a fundamental quantity.
- This set consists of all fundamental quantities and is valid.
6. **Conclusion**:
- The only set that cannot be considered a list of fundamental quantities is **Option A: Length, Mass, and Velocity**.
### Final Answer:
The set that cannot enter into the list of fundamental quantities in any system of units is **Option A: Length, Mass, and Velocity**.
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