(A): A point charge is lying at the centre of a cube of each side. The electric flux emanating from each surface of the cube is `(1^(th))/(6)` total flux.
(R ): According to Gauss theorem, total electric flux through a closed surface enclosing a charge is equal to `1//epsi_(0)` times the magnitude of the charge enclosed.

Options

A. Both .A. and .R. are true and .R. is the correct explanation of .A.
B. Both .A. and .R. are tru and .R. is not the correct explanation of .A.
C. A. is true and .R. is false
D. A. is false and .R. is true

Answer

To solve the problem, we need to analyze the statements given in the assertion (A) and reason (R) and determine their validity based on the principles of electrostatics, particularly Gauss's law.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a point charge \( Q \) located at the center of a cube with each side of length \( l \).
- The cube has a total surface area of \( 6l^2 \) since it has 6 faces.

2. **Applying Gauss's Law**:
- According to Gauss's law, the total electric flux \( \Phi \) through a closed surface is given by:
\[ \Phi = \frac{Q}{\epsilon_0} \]
- Here, \( \epsilon_0 \) is the permittivity of free space.

3. **Calculating the Total Flux**:
- Since the charge is at the center of the cube, the total electric flux through the entire surface of the cube is \( \Phi \).

4. **Flux Through Each Face of the Cube**:
- The electric flux is uniformly distributed through the 6 faces of the cube. Therefore, the flux through each face \( \Phi_{\text{face}} \) is:
\[ \Phi_{\text{face}} = \frac{\Phi}{6} = \frac{Q}{6\epsilon_0} \]
- This means the flux through each surface of the cube is indeed \( \frac{1}{6} \) of the total flux, confirming the assertion (A).

5. **Evaluating the Reason (R)**:
- The reason (R) states that according to Gauss's theorem, the total electric flux through a closed surface enclosing a charge is equal to \( \frac{Q}{\epsilon_0} \).
- This statement is true and aligns with Gauss's law.

6. **Conclusion**:
- Both the assertion (A) and reason (R) are true.
- However, the reason (R) does not provide a direct explanation for the assertion (A) since it does not specifically address the distribution of flux across the surfaces of the cube.
- Therefore, while both statements are true, R does not explain A.

### Final Answer:
- Both assertion (A) and reason (R) are true, but R is not the correct explanation for A.