Step 1: Understanding the Concept:
The discovery and study of Hampi, the ruined capital of the Vijayanagara Empire, is a milestone in Indian historical archaeology.
Step 2: Detailed Explanation:
Statement A is correct: The ruins of Hampi were formally "discovered" and brought to light in 1800 by Colin Mackenzie.
Statement B is correct: Colonel Colin Mackenzie, who was an engineer and antiquarian, created the first detailed survey map of the site.
Statement C is correct: Since the site was in ruins, Mackenzie relied on the oral traditions and memories of the local temple priests of the Virupaksha and Pampadevi shrines to identify buildings.
Statement D is incorrect: Photographers actually began recording Hampi much earlier, starting around 1856 (e.g., Alexander Greenlaw).
Statement E is incorrect: The systematic collection of inscriptions (epigraphy) at the site by the Archaeological Survey of India began in 1836, not 1936.
Step 3: Final Answer:
Statements A, B, and C are historically accurate. Thus, option (a) is the correct answer.