Correct statements among the following is /are :-

Options

A. 2nd electron gain enthalpy is always endothermic
B. Electronegativity is the property of bonding of atoms
C. `Al_(2)O_(3)` and BeO are amphoteric oxide
D. None of these are incorrect

Answer

To solve the question regarding the correctness of the statements provided, we will analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement 1:** "The second electron gain enthalpy is always endothermic."

- **Explanation:** The second electron gain enthalpy refers to the energy change when an electron is added to a negatively charged ion. For example, in the case of oxygen:
- The first electron gain enthalpy (O + e⁻ → O⁻) is exothermic, with a value of -141 kJ/mol, indicating energy is released.
- The second electron gain enthalpy (O⁻ + e⁻ → O²⁻) is endothermic, with a value of +780 kJ/mol, indicating energy is absorbed due to increased electron-electron repulsion.

Thus, this statement is **correct**.

### Step 2: Analyze the second statement
**Statement 2:** "Electronegativity is the property of a bonding of atoms."

- **Explanation:** Electronegativity is defined as the tendency of an atom to attract shared electrons in a chemical bond. It is indeed a property that describes how atoms interact in a bond, such as in H₂ (where electrons are shared equally) versus HCl (where electrons are pulled closer to Cl due to its higher electronegativity).

Thus, this statement is also **correct**.

### Step 3: Analyze the third statement
**Statement 3:** "Al₂O₃ and BeO are amphoteric in nature."

- **Explanation:** Amphoteric oxides can react with both acids and bases.
- Al₂O₃ reacts with acids (like HCl) to form AlCl₃ and with bases (like NaOH) to form sodium aluminate.
- BeO also reacts with acids (forming BeCl₂) and bases (forming beryllium hydroxide).

Both oxides exhibit amphoteric behavior, making this statement **correct**.

### Step 4: Analyze the fourth statement
**Statement 4:** "All the above statements are correct."

- Since we have established that statements 1, 2, and 3 are all correct, this statement is also **correct**.

### Conclusion
All statements provided in the question are correct. Therefore, the answer is:

**Correct statements among the following are: 1, 2, 3, and 4.**