Viceroy, Governor-General, and Secretary of State — Don't Mix Them Up

This is one of the most common sources of confused answers in objective papers, because all three roles look similar on paper ("the top British official for India") but sit in entirely different constitutional locations.

• Governor-General of India was the title under which the officeholder ran the government of British India proper — the provinces directly administered by the Crown (later, by the Crown through the India Office). In this capacity he presided over his Executive Council, dealt with the Imperial Legislative Council, and answered administratively for the day-to-day governance of British Indian territory, much as a head of government would.
• Viceroy of India was the same individual, but this hat was about representing the British monarch personally, especially in relations with the princely states — the roughly 500-plus nominally sovereign states (Hyderabad, Mysore, Kashmir, Baroda, the Rajput states, and so on) that had signed subsidiary or paramountcy treaties with the Crown rather than being annexed outright. As Viceroy, he was the channel of "paramountcy" — the doctrine that ultimate authority over the princely states rested with the Crown, exercised through the Viceroy's political department and the network of Residents and Political Agents stationed at princely courts. A useful shorthand for objective questions: Viceroy = Crown's man for the princely states and diplomatic/ceremonial functions; Governor-General = head of the government of British India for administered territory. After 1858 every appointee held both titles simultaneously, which is precisely why the two get used almost interchangeably in casual writing — but a precise exam answer should know which hat is functionally relevant to a given event (e.g., a princely-state merger or Instrument of Accession question is a "Viceroy" function; a Legislative Council debate is a "Governor-General" function).
• Secretary of State for India is a completely different post and is very frequently confused with the Viceroy in objective questions. The Secretary of State was a British Cabinet minister sitting in London, accountable to the British Parliament, and was created by the Government of India Act, 1858 to replace the Company's Court of Directors and Board of Control. He (there was no woman in the post in this period) was the political superior of the Viceroy — instructions on major policy flowed from the India Office in Whitehall to Government House in Calcutta/Delhi, and the Secretary of State could overrule the Viceroy, though in practice a great deal of day-to-day discretion was left to the man on the spot given the months-long communication lag before the telegraph, and even after it. He was assisted by the Council of India, a body of advisors in London (distinct from the Viceroy's Executive Council in India). Exam traps to watch for: (a) the Secretary of State was based in London, not India — never place him "in India"; (b) he was answerable to the British Parliament, while the Viceroy/Governor-General was answerable to the Secretary of State and, formally, to the Crown — not directly to Parliament; (c) famous Secretaries of State whose names get mixed into Viceroy questions include Charles Wood (of Wood's Despatch, 1854, on education — note this predates the post's 1858 creation and was actually issued as President of the Board of Control, a frequent hair-splitting question), Lord Morley (of the Morley-Minto reforms, where Morley was Secretary of State in London and Minto was Viceroy in India — a classic paired-name trap), Edwin Montagu (of the Montagu-Chelmsford reforms, London and India respectively), and Lord Pethick-Lawrence (who led the Cabinet Mission of 1946 to India, working alongside Viceroy Wavell). Whenever a question pairs two surnames joined by a hyphen (Morley-Minto, Montagu-Chelmsford), the first name is almost always the London-based Secretary of State and the second the India-based Viceroy.