Analogous structures are a result of -

Convergent evolution

The correct answer is Option (3) → 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.

Natural selection is a mechanism of evolution. Organisms that are more adapted to their environment are more likely to survive and pass on the genes that aided their success. This process causes species to change and diverge over time.

During his journey, Darwin visited the Galapagos Islands, where he observed an incredible diversity of creatures. He was particularly fascinated by small black birds, which were later named Darwin's Finches. He realized that there were many varieties of finches in the same island. All the varieties, he conjectured, evolved on the island itself. From the original seed-eating features, many other forms with altered beaks arose, enabling them to become insectivorous and vegetarian finches . This process of evolution of different species in a given geographical area starting from a point and literally radiating to other areas of geography (habitats) is called adaptive radiation. Darwin’s finches represent one of the best examples of this phenomenon. Another example is Australian marsupials.