The correct option is
A no article required, no article required
We never use articles before the proper nouns until the proper nouns are used as adjectives.
For example:
1. The Cricket match was great today.
2. Cricket is my favourite sport.
In the first example, 'cricket' is used as an adjective to describe 'match'. Hence we can use 'the' there. However, in the second example, no article is used as 'cricket' is used as a proper noun.
In the same way, in the given sentence, both 'badminton' and 'tennis' are used as proper nouns and hence we can't use any articles before them.
Thus option A is the correct answer.
Options B, C and D are incorrect.