1. Do you want to know more.

2. Do you want to know a lot.
3. Do you want to know a lot of things.
4. Do you want to know effectively.
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Are they all grammatical? The verb 'know' is used as a pronoun and as a verb. Then what is the part of speech of 'more' in #1? What is the part of speech of 'a lot' in #2? A pronoun or an adverb?

All 4 are grammatically correct, yes.

"to know" is a verb in its infinitive form. Verbs are not pronouns.

The words "more" and "lot" are serving as direct objects in 1, 2,and 3. They are not pronouns or adverbs.

In 4, "effectively" is an adverb.

Thank you for your help. I corrected errors.

1. Do you want to know more.
2. Do you want to know a lot.
3. Do you want to know a lot of things.
4. Do you want to know effectively.
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Are they all grammatical? The verb 'know' can be used as a transitive verb or as an intransitive verb. Then what is the part of speech of 'more' in #1? What is the part of speech of 'a lot' in #2? A pronoun or an adverb?
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Then do you mean 'more' is a pronoun?

The word "more" is not a pronoun. Basically it's an adjective that indicates an amount of something or an adverb that indicates the comparative degree of another adjective or adverb.

They had more pizza than they could eat. (adj)
She was more talkative than I remembered. (adv)
He is more handsome than his actor friend. (adv)

http://www.onelook.com/?w=more&ls=a

Once in a while, it will be used on its own -- as if it were the noun (as in my first example above).

1. "Do you want to know more?" - In this sentence, "more" is used as an adverb modifying the verb "know." It is specifying that the person wants to know to a greater extent or have a greater understanding of something.

2. "Do you want to know a lot?" - In this sentence, "a lot" is used as a pronoun. It serves as the object of the verb "know," indicating that the person wants to have a substantial amount of knowledge or information.

3. "Do you want to know a lot of things?" - Here, "a lot of things" functions as a noun phrase. The word "a lot" functions as a determiner, modifying the noun "things." It indicates that the person wants to acquire a large quantity or range of knowledge or information.

4. "Do you want to know effectively?" - In this sentence, "effectively" is used as an adverb modifying the verb "know." It is suggesting that the person wants to acquire knowledge or information in an efficient or productive manner.