Assertion : Two non-ideal batteries are connected in parallel with same polarities on same: side. The equivalent emf is smaller than either of the two emfs.
Reason : Two non-ideal batteries are connected in parallel, the equivalent inter resistance is smaller than either of the two internal resistances.

Options

A. It both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. It both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. It Assertion is true, but the Reason is false.
D. It Assertion is false but the Reason is true.

Explanation

To solve the problem, we need to analyze the assertion and reason provided regarding the behavior of two non-ideal batteries connected in parallel.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that when two non-ideal batteries are connected in parallel with the same polarity, the equivalent EMF is smaller than either of the two EMFs.
- Non-ideal batteries have internal resistance, which affects the overall EMF when connected in parallel.

2. **Understanding the Reason**:
- The reason states that when two non-ideal batteries are connected in parallel, the equivalent internal resistance is smaller than either of the two internal resistances.
- This is based on the principle that for resistances in parallel, the equivalent resistance is always less than the smallest individual resistance.

3. **Calculating Equivalent EMF**:
- For two batteries with EMFs \(E_1\) and \(E_2\) and internal resistances \(R_1\) and \(R_2\), the equivalent EMF (\(E_{eq}\)) can be calculated using the formula:
\[ E_{eq} = \frac{E_1/R_1 + E_2/R_2}{1/R_1 + 1/R_2} \]
- This formula indicates that the equivalent EMF depends on the ratio of EMFs to their internal resistances.

4. **Analyzing the Conditions**:
- If the internal resistances \(R_1\) and \(R_2\) are significant compared to the EMFs, it is possible for the equivalent EMF to be less than either \(E_1\) or \(E_2\).
- However, it is also possible for \(E_{eq}\) to be greater than one of the individual EMFs depending on the values of \(E_1\), \(E_2\), \(R_1\), and \(R_2\).

5. **Conclusion on Assertion**:
- Since the equivalent EMF can be either smaller or greater than the individual EMFs depending on the specific values, the assertion is **false**.

6. **Conclusion on Reason**:
- The reason is correct because the equivalent internal resistance for two resistances in parallel is indeed less than either of the individual resistances.

7. **Final Answer**:
- The assertion is false, and the reason is true. Therefore, the correct option is **D**.