Match List-I with List-II:

(A) Alexander Greenlaw          (I) Documenting the inscriptions on the temple walls

(B) John Marshall                      (II) Visits Vijayanagara in 1800

(C) J.F. Fleet                                (III) Conservation works of Vijayanagara began under him

(D) Colin Mackenzie                (IV) Detailed photography at Hampi

Choose the correct answer from the options given below:

The correct answer is (A) - (IV), (B) - (III), (C) - (I), (D) - (II).

To understand why this is the correct match, let us look at the historical contributions of each individual to the study and conservation of the ruins of Hampi (Vijayanagara):

(A) Alexander Greenlaw - (IV) Detailed photography at Hampi
Alexander Greenlaw, a British military officer, took the first detailed photographs of the ruins of Hampi in 1856. His plaster-of-Paris negatives became an invaluable historical record for archaeologists and conservationists to study the original state of the structures before decay and subsequent reconstructions.

(B) John Marshall - (III) Conservation works of Vijayanagara began under him
As the Director-General of the Archaeological Survey of India (ASI) in the early 20th century, Sir John Marshall initiated systematic conservation and documentation efforts at Vijayanagara, ensuring the preservation of key monuments at the site.

(C) J.F. Fleet - (I) Documenting the inscriptions on the temple walls
John Faithful Fleet was an epigraphist and historian who made significant contributions by systematically copying, translating, and documenting the numerous Sanskrit and Kannada inscriptions found on the temple walls of Vijayanagara, which helped reconstruct the political history of the empire.

(D) Colin Mackenzie - (II) Visits Vijayanagara in 1800
Colonel Colin Mackenzie, a surveyor and antiquarian, visited the ruins of Vijayanagara in 1800. He prepared the first source map of the site and collected oral histories and historical manuscripts associated with the ruins, bringing the site to light for modern scholarship.

Matching these points confirms the correct option as:
(A) - (IV), (B) - (III), (C) - (I), (D) - (II).