Question

She enjoys _____ badminton.

Answer 1

Option (C).

She enjoys playing badminton.

What is playing?

The term "playing" means the act of taking part in a game or sport.

What is badminton?

The "badminton" is a sport in which light rackets are used to volley an object—called a shuttlecock, shuttle, birdie, or bird—back and forth over a high net.

She enjoys playing badminton. Here to is infinitive. and gerund is adding 'Ing' to verb play. 'play + Ing' = playing.

To learn more about badminton here

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Answer 2

Hello,

She enjoys playing badminton.

Some verbs like "enjoy" are normally followed by the -ing form, not the to-infinitive