Assertion : Binding energy per unit nucleon increase in atomic mass number .
Reason : Density of nucleus increases with increase in mass number.

Answer

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "Binding energy per unit nucleon increases with atomic mass number."
- Binding energy (BE) is defined as the energy required to disassemble a nucleus into its constituent nucleons. The binding energy per nucleon is calculated by dividing the total binding energy by the mass number (A).
- As mass number increases, the binding energy per nucleon does not continuously increase. It increases up to iron (Fe, mass number ~56) and then starts to decrease for heavier elements. Therefore, the assertion is not entirely true.

2. **Understanding the Reason**:
- The reason states that "Density of nucleus increases with increase in mass number."
- The density (D) of a nucleus is given by the formula:
\[ D = \frac{A}{\frac{4}{3} \pi r^3} \]
where \( r \) (the radius of the nucleus) can be approximated as \( r_0 A^{1/3} \).
- Substituting \( r \) into the density formula gives:
\[ D = \frac{A}{\frac{4}{3} \pi (r_0 A^{1/3})^3} = \frac{A}{\frac{4}{3} \pi r_0^3 A} = \frac{3}{4 \pi r_0^3} \]
- This shows that the density of the nucleus remains approximately constant as mass number increases, because the mass number \( A \) cancels out. Hence, the reason is also incorrect.

3. **Conclusion**:
- Both the assertion and the reason are incorrect. Therefore, the correct answer to the question is that both the assertion and reason are false.