`{:("Convergent evolution","Divergent evolution"),((1)"Bones of forelimbs of vertebrates","Wings of butterfly and birds"),((2)"Thorns of Bougainvillia and tendrils of Cucurbita","Eyes of Octopus and Mammals"),((3)"Eyes of octopus and mammals","Bones of forelimbs of vertebrates"),((4)"Thorns of Bougainvillia and tendrils of Cucurbita","Wings of butterflies and birds"):}`

Answer

To solve the question regarding convergent and divergent evolution, we need to understand the definitions of both concepts and analyze the given pairs accordingly.

### Step-by-Step Solution:

1. **Define Convergent Evolution**:
- Convergent evolution occurs when unrelated organisms develop similar traits or structures (analogous structures) due to adapting to similar environments or ecological niches. These structures serve similar functions but do not share a common evolutionary origin.

2. **Define Divergent Evolution**:
- Divergent evolution occurs when related organisms develop different traits or structures (homologous structures) due to adapting to different environments or ecological niches. These structures may serve different functions but share a common evolutionary origin.

3. **Analyze Each Pair**:
- **(1) Bones of forelimbs of vertebrates**: These are homologous structures that have evolved from a common ancestor but have adapted to different functions (e.g., human arm, whale flipper). This is an example of divergent evolution.
- **(1) Wings of butterfly and birds**: These are analogous structures that serve the same function (flight) but evolved independently in different lineages. This is an example of convergent evolution.

- **(2) Thorns of Bougainvillea and tendrils of Cucurbita**: Both structures are adaptations for protection and support, respectively, but they come from different plant families. This indicates divergent evolution.
- **(2) Eyes of octopus and mammals**: These eyes have similar functions (vision) but evolved independently in two unrelated groups. This is an example of convergent evolution.

- **(3) Eyes of octopus and mammals**: As mentioned, this is convergent evolution due to the independent evolution of similar structures for the same function.
- **(3) Bones of forelimbs of vertebrates**: As previously stated, this is divergent evolution.

- **(4) Thorns of Bougainvillea and tendrils of Cucurbita**: This is divergent evolution as they have different functions but similar structural adaptations.
- **(4) Wings of butterflies and birds**: This is convergent evolution as they serve the same function but evolved independently.

4. **Select the Correct Pair**:
- From the analysis, the correct pairs are:
- **(1)**: Bones of forelimbs of vertebrates - Divergent evolution
- **(2)**: Eyes of octopus and mammals - Convergent evolution
- **(3)**: Eyes of octopus and mammals - Convergent evolution
- **(4)**: Wings of butterflies and birds - Convergent evolution

The only correct pair that fits the definitions is **(2)**: Eyes of octopus and mammals (convergent evolution).

### Final Answer:
The correct pair of convergent evolution and divergent evolution is **(2) Eyes of octopus and mammals (convergent evolution)**.