STATEMENT-1 `:` When two isolated charged metal spheres are touched with each other potential energy of system may decrease.
and
STATEMENT-2 `:` There may be transfer of charge from one to other after touching.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To solve the given problem, we need to analyze both statements and determine their validity based on the principles of electrostatics.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have two isolated charged metal spheres, Sphere 1 with charge \( Q_1 \) and Sphere 2 with charge \( Q_2 \).
- Each sphere has a certain potential due to its charge.

2. **Potential of Each Sphere**:
- The potential \( V \) of a charged sphere is given by the formula:
\[ V = \frac{k \cdot Q}{r} \]
where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( r \) is the radius of the sphere.
- If \( V_1 \) (potential of Sphere 1) is greater than \( V_2 \) (potential of Sphere 2), then \( V_1 > V_2 \).

3. **Touching the Spheres**:
- When the two spheres are touched, they come to the same potential because they are conductors. This means charges will redistribute between the two spheres until \( V_1 = V_2 \).

4. **Charge Transfer**:
- Due to the difference in potential, charge will flow from the sphere with higher potential to the sphere with lower potential until equilibrium is reached.
- This transfer of charge can lead to a change in the total charge on each sphere.

5. **Potential Energy Change**:
- The potential energy \( U \) of a system of charges can be expressed as:
\[ U = \frac{1}{2} \sum_{i} \frac{Q_i^2}{C_i} \]
where \( C_i \) is the capacitance of each sphere.
- As the charges redistribute, the potential energy of the system may decrease because the system moves towards a state of lower potential energy.

6. **Conclusion**:
- Since there is a transfer of charge and the potential energy of the system may decrease, both statements are correct.
- Therefore, the conclusion is that the potential energy of the system may decrease when two isolated charged metal spheres are touched, and there is indeed a transfer of charge.

### Final Answer:
Both statements are correct.