When do you use duquel, lequel, and auquel? And other variations of those?

For instance, what would this be and why?

Nous entendons beaucoup parler de projets communautaires?

__________ entendez-vous parler?

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Let's begin with the Relative Pronouns "lequel (masc. sing), laquelle (fem. sing.), lesquels (masc. plural) and lesquelle3s (fem. plural.)" They all mean "which" as the object of a preposition and are used principally for things.

Examples:

C'est la porte par "laquelle" il est sorti.
That's the door through which he left.

Voici le bureau sur "lequel" j'ai laissé mes lunettes.
Here is the desk on which I left my glasses.

Now, the Interrogatives.

which? what? (adjective) = quel, quelle, quels, quelles

which? which one(s)? (pronoun) = lequel, laquelle, lesquels, lesquelles.

Lequel de ces chapeaux est le plus cher?
Which (one) of these hats is the most expensive?

NOTE: the pronoun "lequel" agrees in gender and number with the noun it replaces.

When "à" and "de" are used before the forms of "lequel", the usual contractions take place.

singular = auquel, à laquelle / duquel, de laquelle

plural = aauxquels, auxquelles / desquels, desquelles

Examples:

Auquel de tes amis as-tu-écrit?
To which of your friends did you write? (OR Which of your friends did you write to?)

De quels enfants est-il fier? Desquels est-il fier?
Of which children is he proud? Of which ones is he proud?

Now, in the question: "Nous entendons beaucoup parler de projets communautaires?"

NOTE the preposition "de" because the pronoun "en" replaces "de + noun" and generally refers to things. It is usually translated into English by "some, any, of it (them), from there."

"En" is always expressed in French, even though its equivalent may not be expressed in English. "En" must be used when the noun is omitted after a number, an adverb or noun of quantity, or an idiom requiring "de."

Voici des framboises. En voulez-vous?
Here are some raspberries. Do you want some?

Elle n'en a pas acheté.
She didn't buy any. (She bought none.)

N'en parlons plus.
Let's not speak of it any more.

Vient-il de la ville? Oui, il en vient.
Does he come from the city? Yes, he does (come from there.)

The other pronoun "y" always refers to things or places and it generally replaces "à + noun" but may also replace other prepositions of position, such as "chez, dans, en, sous, or sur + noun."

Both these pronouns regularly precede the verb, except in the affirmative imperative, where they follow.

Mme

To determine which relative pronoun to use in French, such as "duquel," "lequel," and "auquel," you need to consider the preposition that follows it and the noun it is referring to. Here's a breakdown of when to use each:

1. "Duquel" is used after the prepositions "de" or "d'" when referring to a masculine singular noun.

Example: L'homme duquel je te parle (The man about whom I'm talking)

2. "Lequel" is used after prepositions such as "à," "sur," "dans," "avec," and others when referring to both masculine and feminine singular nouns.

Example: La maison dans laquelle j'habite (The house in which I live)

3. "Auquel" is used after prepositions such as "à," "sur," "dans," "avec," and others when referring to a masculine singular noun preceded by the preposition "à."

Example: Les personnes auxquelles je parle (The people to whom I am talking)

In the given example sentence, "Nous entendons beaucoup parler de projets communautaires?" (We hear a lot about community projects?), the question asks "Whom do you hear talking?" In this sentence, "vous" refers to the second person plural (you all).

To fill in the blank, you will use the appropriate form of the pronoun "de quel" depending on the context. Since the sentence includes the preposition "de," indicating possession, and refers to a plural "projets communautaires," you would use the plural form "desquels":

"Desquels entendez-vous parler?" (About which ones do you hear talking?)

Here, "desquels" combines the preposition "de" with the pronoun "lesquels" to indicate a plural and masculine noun in the plural form.