if work done by a conservative force is positive the select the correct option(s).
(a) potential energy will decrease.
(b) potential energy may increase or decrease.
(c )kinetic energy will increase.
(d) kinetic energy may increase or decrease.

Explanation

To solve the question, we need to analyze the relationship between work done by a conservative force, potential energy, and kinetic energy.

### Step-by-Step Solution:

1. **Understanding Work Done by Conservative Forces**:
- A conservative force is one where the work done is independent of the path taken and depends only on the initial and final positions.
- The work done \( W \) by a conservative force can be expressed in terms of potential energy \( U \) as:
\[ W = -\Delta U = U_i - U_f \]
where \( U_i \) is the initial potential energy and \( U_f \) is the final potential energy.

2. **Analyzing Positive Work**:
- If the work done by the conservative force is positive (\( W > 0 \)), it implies:
\[ U_i - U_f > 0 \implies U_i > U_f \]
- This means that the potential energy decreases as the object moves under the influence of the conservative force.

3. **Conclusion about Potential Energy**:
- From the analysis, we conclude that if the work done by a conservative force is positive, the potential energy will decrease.
- Therefore, option (a) "potential energy will decrease" is correct.

4. **Analyzing Kinetic Energy**:
- The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy:
\[ W = \Delta K = K_f - K_i \]
- Since we have established that the work done is positive, this means that the change in kinetic energy \( \Delta K \) could be positive, negative, or zero depending on the initial and final kinetic energies.
- Thus, kinetic energy may increase or decrease.

5. **Conclusion about Kinetic Energy**:
- Therefore, option (d) "kinetic energy may increase or decrease" is also correct.

### Final Answer:
The correct options are:
- (a) Potential energy will decrease.
- (d) Kinetic energy may increase or decrease.