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How to use the words such as "remain and remaining" in sentence appropriately?

"Remain" is a verb that means "continue to be / act" (for example, "Please remain in your seats until the captain has switched off the seatbelt sign" or "They remained British citizens even though they lived for 40 years in the USA." The adjective "remaining" means "what is left after something happens." For example, "The remaining food was thrown away after the party." We can also use "remain" in this way, but then we need to add the preposition "of": "After the earthquake, very little remained of the village."

Remain can be used to mean different things.
1. To be left when the other parts have gone or have been used 'Only two minutes still remain (are left) in the game'
2. To be something that still needs to be done. 'Much work remains to be done.' (There is still alot of work to do)
3. To stay in the same place/ with the same person or group or to stay after others have left.'She remained in Boston after she finished college) Today we often use 'stay' in this sense.
4. To stay in a specified state, condition or position 'She remained calm).' (kept or stayed)
5. To continue to be something. 'They have remained friends.' (They are still friends)
For meanings 3,4, and 5 we can use also use 'stay'
'Remaining' is a participle which we use as an adjective to modify nouns mostly to describe something that is left to do or something/ someone that is left when the rest have gone/been used.
'Remaining' can come before or after the noun it modifies. 'There is a lot of work remaining' (remaining modifies 'work') 'They tried to sell the remaining books.' (remaining modifies chicken)