Analogous structures are a result of:

Convergent evolution

The correct answer is Option (2) → Convergent evolution

Analogy is based on convergent evolution.Wings of butterfly and of birds look alike. They are not anatomically similar structures though they perform similar functions. Hence, analogous structures are a result of convergent evolution - different structures evolving for the same function and hence having similarity. Other examples of analogy are the eye of the octopus and of mammals or the flippers of Penguins and Dolphins.

Homology is based on divergent evolution .Homology indicates common ancestry. They perform different functions but  have similar anatomical structure –examples are vertebrate hearts or brains. In plants also, the thorn and tendrils of Bougainvillea and Cucurbita represent homology.

Genetic drift: Random changes in allele frequencies in small populations due to chance events can lead to significant changes over time.

Mutation arise due to change in a single base pair of DNA is known as point mutation. A classical example of such a mutation is sickle cell anemia.