Joseph introduced me . . . . . . . his mother as the best batsman.

The correct answer is: A. to

Joseph introduced me to his mother as the best batsman.

The preposition “to” is used to introduce someone to someone else. In this case, Joseph is introducing the speaker to his mother.

The other options are not correct because they do not make sense in the context of the sentence.

• The preposition “by” is used to indicate the means by which something is done. For example, “The painting was done by Picasso.”
• The preposition “for” is used to indicate the purpose of something. For example, “I bought this book for my son.”
• The preposition “with” is used to indicate the company of someone. For example, “I went to the movies with my friends.”