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Hi.

In "What kind/kinds of NOUN....?" do the words 'kind/kinds' always have to correspond to the number of the NOUN? That is, when the NOUN is singular, do we have to choose 'kind' and when the NOUN is plural, do we have to choose 'kinds'?

(1)What kind of film do you like? (singular -- singular)
(2)What kinds of films do you like? (plural -- plural)
(3)What kind of films do you like? (singular -- plural)
(4)What kinds of film do you like? (plural -- singular)

Are (3) and (4) wrong?

Thank you.
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It is not a matter of correspondence with the number of the noun object. All are acceptable, at least informally, and all are certainly in use in the spoken language, almost indiscriminately. (1) and (3) are soliciting a response of a single sort, while (2) and (4) leave it more open to the respondent to supply several types of film(s). Swan prefers the singular object of the preposition, that is (1) or (4).
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what is kinds of speech
Kinds of Speech are

Noun

Pronoun

Verb

Adverb

Adjective

Preposition

Conjuction

Interjection