The Census of India, 2011, outlines the characteristics of an urban agglomeration as follows:
(A) A continuous urban spread comprising a town and its adjacent outgrowths: This statement accurately defines an urban agglomeration. Thus, (A) is valid.
(C) Two or more contiguous towns, with or without outgrowths: This also describes an urban agglomeration, where proximate towns combine. Therefore, (C) is valid.
(B) Urban settlements combined with one rural settlement: This scenario does not characterize an urban agglomeration. Consequently, (B) is invalid.
(D) Urban villages encompassed within a metropolitan area: This refers to a distinct concept, not directly defining an urban agglomeration. Hence, (D) is invalid.
The correct classifications are therefore (A) and (C).