The correct sentence is "Franklin Delano Roosevelt, who was elected the thirty-second president of the United States, was born in 1882.
Nominative pronouns function as the subject of the sentence. This is why they are also known as subjective pronouns. Common nominative pronouns are I, you (both singular and plural), he, she, it, we, they and who.
Objective pronouns are used when something is being done to the subject. Common objective pronouns are me, you (both singular and plural), him, her, it, us, them and whom.
In the given sentence, the correct pronoun is "who". It is a nominative pronoun.
The subject in this sentence is Franklin Delano Roosevelt, and since the pronoun refers to him, it has to be nominative. Of the given options, "who" is the nominative pronoun and thus it is correct.
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