What do you understand by analogous organs?

The correct answer is Option (2) → Anatomically different but performing similar functions.

Comparative anatomy compares the structure of organs with the job they do. When the structure is the same but the job differs, the organs are homologous; when the structure differs but the job is the same, they are analogous.

Option (1) Anatomically similar but performing different functions. — Incorrect. Organs that are anatomically similar but do different jobs are homologous, like the forelimbs of whales, bats, cheetah and human.

Option (2) Anatomically different but performing similar functions. — Correct. Analogous organs are not anatomically similar, yet they perform similar functions, like the wings of a butterfly and of a bird. They are a result of convergent evolution.

Option (3) Anatomically similar and functionally similar. — Incorrect. Organs similar in both structure and function do not show the contrast that defines either homology or analogy.

Option (4) Anatomically different and functionally different. — Incorrect. Organs different in both structure and function have nothing in common to compare, so they are neither homologous nor analogous.

NCERT Extract:
What are the Evidences for Evolution? – “… Homology is based on divergent evolution whereas analogy refers to a situation exactly opposite. 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.”