Hello Mooj,
Welcome to Apple Support Communities. It looks like music starts playing randomly on your iPad, and we'd be happy to look into this with you.
If your iPad automatically playing music randomly or when you plug in your headphones, you might have the music app running in the background that is playing music. Closing that app should stop music from automatically playing.
How to force an app to close on your iPhone, iPad, or iPod touch
Next, let's make sure your iPad is up-to-date on software, so if you haven’t updated yet, let’s do so now.
How to back up your iPhone, iPad, and iPod touch
Update your iPhone, iPad, or iPod touch
If the issue persists, deleting the Music app, and reinstalling it from the App Store would be the next step:
Delete apps from iPad
Download apps and games on your iPhone or iPad
We'd recommend creating a backup of your iPad as explained above before trying any steps to protect your data.
We hope this information is useful. Kind regards.