In income-tax jurisprudence on the scope of 'business' and 'profession', consider the following…

Both I and II are correct. In income-tax law 'business' is the wider term: a profession is an occupation carried on for gain and so falls within the wider notion of business, whereas a business counts as a profession only when its income depends mainly on the specialised intellectual skill and personal qualifications of the person carrying it on. Hence every profession is a business, but not every business is a profession.