Mark the correct statements `(s)`.

Options

A. if speed of a body is varying, its velocity must be varying and it must have zero acceleration
B. if velocity of a body is varying, its speed must be varying
C. a body moving with varying velocity may have a constant speed
D. a body moving with varying speed may have constant velocity if its direction of motion remains constant.

Explanation

To solve the question of marking the correct statements regarding speed and velocity, we will analyze each statement based on the definitions and properties of speed and velocity.

### Step-by-Step Solution:

1. **Understanding Speed and Velocity**:
- Speed is a scalar quantity that only has magnitude (e.g., 10 m/s).
- Velocity is a vector quantity that has both magnitude and direction (e.g., 10 m/s east).

2. **Analyzing Statement 1**:
- **Statement**: If the speed of a body is varying, then its velocity must be varying and it must have zero acceleration.
- **Analysis**: This statement is incorrect. Speed can vary while the direction remains constant, resulting in constant velocity. Additionally, if speed is changing, acceleration cannot be zero.
- **Conclusion**: **False**

3. **Analyzing Statement 2**:
- **Statement**: If the velocity of a body is varying, its speed must be varying.
- **Analysis**: This statement is also incorrect. Velocity can vary due to a change in direction while maintaining constant speed (e.g., an object moving in a circle at constant speed).
- **Conclusion**: **False**

4. **Analyzing Statement 3**:
- **Statement**: A body moving with varying velocity may have a constant speed.
- **Analysis**: This statement is true. A body can have varying velocity if the direction changes while the speed remains constant (e.g., uniform circular motion).
- **Conclusion**: **True**

5. **Analyzing Statement 4**:
- **Statement**: A body moving with varying speed may have constant velocity if its direction of motion remains constant.
- **Analysis**: This statement is true. If the speed varies but the direction remains constant, the velocity can still be considered constant in terms of direction, but the magnitude of the velocity will change.
- **Conclusion**: **True**

### Final Marking of Statements:
- **Statement 1**: False
- **Statement 2**: False
- **Statement 3**: True
- **Statement 4**: True