Step 1: Recognise the disease. A child who develops skin eruptions (severe photosensitivity, sunburn, freckling, and a high risk of skin cancers) on exposure to sunlight, due to an inherited DNA repair defect, has Xeroderma Pigmentosum (XP).
Step 2: Link the disease to its repair pathway. Ultraviolet (UV) light in sunlight produces pyrimidine (thymine) dimers - covalent bonds between adjacent pyrimidines that distort the DNA helix. These bulky lesions are removed by the Nucleotide Excision Repair (NER) pathway. In XP, the genes coding for NER enzymes are mutated, so UV-induced dimers accumulate, leading to mutations, photosensitivity, and markedly increased skin cancer risk. Hence the defect is in nucleotide excision repair.
Step 3: Why the other options are wrong. Base excision repair (BER) corrects single damaged or modified bases (e.g. from oxidation, deamination, depurination), not bulky UV dimers. Mismatch repair (MMR) corrects base-base mismatches and insertion/deletion loops arising during replication; its defect causes Hereditary Non-Polyposis Colorectal Cancer (Lynch syndrome), not photosensitivity. Recombination/double-strand-break repair defects (e.g. Ataxia telangiectasia, Fanconi anaemia) cause radiosensitivity and other syndromes, not the UV photosensitivity of XP.
Final answer: Option A - Nucleotide excision (repair).