To determine which set cannot enter into the list of fundamental quantities in any system of units, we need to analyze the given options based on the definition of fundamental quantities. Fundamental quantities are those that are independent of other physical quantities.
### Step-by-Step Solution:
1. **Understand Fundamental Quantities**:
- Fundamental quantities are independent quantities that do not rely on other physical quantities for their definition. Examples include length, mass, and time.
2. **Analyze the Options**:
- We are given four sets of quantities. We need to identify which set includes quantities that are dependent on others.
3. **Evaluate Each Set**:
- **Set 1: Length, Mass, and Velocity**:
- Length and mass are fundamental quantities. However, velocity is defined as length divided by time (velocity = length/time). Therefore, velocity depends on both length and time, making this set not entirely fundamental.
- **Set 2: Mass, Time, and Velocity**:
- Mass and time are fundamental quantities. Velocity, again, is dependent on length and time. Thus, this set also includes a dependent quantity.
- **Set 3: Length, Mass, and Time**:
- All three quantities (length, mass, and time) are fundamental and independent of each other. This set can enter the list of fundamental quantities.
- **Set 4: Length, Mass, and Acceleration**:
- Length and mass are fundamental. However, acceleration is defined as the change in velocity over time (acceleration = velocity/time), which means it depends on other quantities. Thus, this set also includes a dependent quantity.
4. **Conclusion**:
- The sets that cannot enter the list of fundamental quantities are those that include velocity or acceleration because they are derived from other quantities. Therefore, the sets containing velocity or acceleration cannot be considered fundamental.
### Final Answer:
The sets that cannot enter into the list of fundamental quantities are:
- Set 1: Length, Mass, and Velocity
- Set 2: Mass, Time, and Velocity
- Set 4: Length, Mass, and Acceleration
The only set that can enter the list of fundamental quantities is:
- Set 3: Length, Mass, and Time
