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A gene is defined as the smallest unit of inheritance that occurs in pairs on chromosomes. Genes are segments of DNA that contain the instructions for the production of proteins, which are crucial for the functioning and development of an organism. Each gene can exist in different forms known as alleles, which affect various traits. In diploid organisms, genes typically occur in pairs, one inherited from each parent, allowing for genetic variation and diversity within a population.

The other options represent important concepts in genetics but do not correctly match the definition provided. The nucleus is the cellular structure that houses the chromosomes, chromosomes are the long strands of DNA that carry many genes, and alleles refer to the different versions of a gene rather than the unit of inheritance itself. Therefore, identifying a gene as the smallest unit of inheritance directly aligns with the fundamental principles of genetic inheritance.