Final answer:
The statement is false; an auxotroph is a nutritional mutant that cannot synthesize a specific nutrient due to a loss-of-function mutation, not a cell requiring auxiliary proteins for DNA replication. Hence, option (2) is correct.
Step-by-step explanation:
The statement that an auxotroph is a cell that requires auxiliary proteins to replicate DNA is false. An auxotroph is a nutritional mutant with a loss-of-function mutation in a gene encoding the biosynthesis pathway of a specific nutrient, such as an amino acid. This defect requires an external source of the specific nutrient for the organism's growth since it cannot synthesize the nutrient itself.
The technique called replica plating is used to detect such auxotrophic mutants in bacteria. Wild-type cells can grow on a medium lacking the specific nutrient because they can synthesize it, but auxotrophs cannot. Growth on a nutritionally complete medium in addition to nutrient-deficient plates is essential to ensure that colonies are being transferred correctly and to identify the presence or absence of growth on various media, thereby determining the auxotrophy.