An object may have
(a). Varying speed without having varying velocity
(b). Varying velocity without having verying speed
(c). Non zero acceleration without having varying velocity
(d). Non zero acceleration without having varying speed.

Options

A. a,b & c are correct
B. b & d are correct
C. a,b & c are correct
D. a & d are correct

Answer

To solve the question, we need to analyze each statement one by one and determine whether it is true or false based on the principles of motion.

### Step-by-Step Solution:

1. **Statement (a): Varying speed without having varying velocity.**
- **Analysis:** Speed is the magnitude of velocity. If the speed is varying, it means the magnitude is changing. Since velocity is a vector that includes both magnitude and direction, a change in magnitude (speed) will result in a change in velocity. Therefore, this statement is **false**.

2. **Statement (b): Varying velocity without having varying speed.**
- **Analysis:** This scenario can occur in circular motion. In uniform circular motion, the object moves with a constant speed, but the direction of the velocity vector changes continuously. Since velocity is a vector, a change in direction means that the velocity is varying even though the speed remains constant. Therefore, this statement is **true**.

3. **Statement (c): Non-zero acceleration without having varying velocity.**
- **Analysis:** Acceleration is defined as the rate of change of velocity. If the velocity is not changing (i.e., it is constant), then the acceleration must be zero. Therefore, it is impossible to have non-zero acceleration without varying velocity. This statement is **false**.

4. **Statement (d): Non-zero acceleration without having varying speed.**
- **Analysis:** This situation can also occur in circular motion. An object moving in a circle at a constant speed has a non-zero centripetal acceleration directed towards the center of the circle, even though its speed remains constant. Therefore, this statement is **true**.

### Conclusion:
Based on the analysis:
- Statement (a) is **false**.
- Statement (b) is **true**.
- Statement (c) is **false**.
- Statement (d) is **true**.

Thus, the correct statements are **(b) and (d)**.