Explain the meanings of the idioms 'to beat about the bush', 'to be carried away', 'to do away with', 'to build castles in the air', and 'to burn the candle at both ends'. Also, identify whether 'run

Here are the meanings of the idioms and the identification of idioms in the sentences:

A. Meanings of the following idioms:

• a) to beat about the bush: To avoid the main topic; to speak indirectly without coming to the point.
• b) to be carried away: To be overcome by strong emotion or enthusiasm, often leading to a loss of self-control.
• c) to do away with: To get rid of something; to abolish or destroy it.
• d) to build castles in the air: To dream or fantasize about impossible or unrealistic plans and hopes.
• e) to burn the candle at both ends: To work or live excessively, exhausting oneself by staying up late and getting up early.

B. Identify which groups of words are used as idioms and which are not in the following sentences:

• a) The battery has run down.
  • run down is an idiom (meaning to lose power).
• b) The boy has run down the hill.
  • run down is not an idiom (meaning to physically descend).
• a) The plane took off at 10 am.
  • took off is an idiom (meaning to depart or become airborne).
• b) He took off his cap as he entered the room.
  • took off is an idiom (meaning to remove something).
• c) It is not good to run down people.
  • run down is an idiom (meaning to criticize or speak badly about someone).