The oxides of group 13 elements are given as
A) `B_2 O_3` B) `Al_2 O_3 ` C) `Ga_2 O_3` D)`"In"_2 O_3`

Options

A. A and B are basic in nature
B. B and C are amphoteric in nature
C. C and D are acidic in nature
D. A and D are neutral

Answer

To solve the question regarding the oxides of group 13 elements, we need to analyze each oxide provided in the options and determine their nature (acidic, basic, or amphoteric).

### Step-by-Step Solution:

1. **Identify the Group 13 Elements**:
The group 13 elements include boron (B), aluminium (Al), gallium (Ga), indium (In), and thallium (Tl). The oxides given in the question are:
- A) \( B_2O_3 \)
- B) \( Al_2O_3 \)
- C) \( Ga_2O_3 \)
- D) \( In_2O_3 \)

2. **Analyze Each Oxide**:
- **\( B_2O_3 \)**: Boron oxide is known to be acidic in nature. Non-metal oxides are typically acidic.
- **\( Al_2O_3 \)**: Aluminium oxide is amphoteric. It can react with both acids and bases.
- **\( Ga_2O_3 \)**: Gallium oxide is also amphoteric, similar to aluminium oxide.
- **\( In_2O_3 \)**: Indium oxide is generally considered to be amphoteric as well.

3. **Determine the Nature of Each Oxide**:
- \( B_2O_3 \): Acidic
- \( Al_2O_3 \): Amphoteric
- \( Ga_2O_3 \): Amphoteric
- \( In_2O_3 \): Amphoteric

4. **Conclusion**:
Based on the analysis, the oxides of group 13 elements can be categorized as follows:
- Acidic: \( B_2O_3 \)
- Amphoteric: \( Al_2O_3 \), \( Ga_2O_3 \), \( In_2O_3 \)

5. **Final Answer**:
The oxides of group 13 elements that are amphoteric are \( Al_2O_3 \) and \( Ga_2O_3 \). Therefore, the correct options are B and C.