To solve the question, we need to identify which set of quantities cannot be classified as fundamental quantities in any system of units. Fundamental quantities are those that are independent of each other, and all other quantities can be expressed in terms of these fundamental quantities.
### Step-by-Step Solution:
1. **Understanding Fundamental Quantities**:
- Fundamental quantities are basic physical quantities that cannot be defined in terms of other quantities. They are independent and serve as the foundation for deriving other physical quantities.
2. **Analyzing the Options**:
- We have four options to evaluate:
1. Length, Mass, and Velocity
2. Length, Time, and Velocity
3. Mass, Time, and Velocity
4. Length, Time, and Mass
3. **Evaluating Option 1: Length, Mass, and Velocity**:
- Length and Mass are fundamental quantities.
- Velocity is defined as distance (length) divided by time. Therefore, velocity depends on length and time.
- Since velocity cannot stand alone as a fundamental quantity (it depends on length and time), this option can be included in the list of fundamental quantities.
4. **Evaluating Option 2: Length, Time, and Velocity**:
- Length and Time are fundamental quantities.
- Velocity is derived from length and time (velocity = length/time).
- Since velocity depends on length and time, this option cannot be included in the list of fundamental quantities.
5. **Evaluating Option 3: Mass, Time, and Velocity**:
- Mass and Time are fundamental quantities.
- Velocity is again dependent on length and time.
- Since velocity cannot be defined using mass and time alone, this option can be included in the list of fundamental quantities.
6. **Evaluating Option 4: Length, Time, and Mass**:
- Length, Time, and Mass are all fundamental quantities.
- None of these can be defined in terms of each other, making them independent.
- Therefore, this option can also be included in the list of fundamental quantities.
7. **Conclusion**:
- The only set that cannot enter into the list of fundamental quantities is **Option 2: Length, Time, and Velocity**.
### Final Answer:
**Option 2: Length, Time, and Velocity cannot enter into the list of fundamental quantities in any system of units.**
