English

The phrase 'broken away from' is a common English phrasal verb meaning to separate or distance oneself from someone or something. The correct preposition to complete the phrase is 'away,' forming 'broken away from his old friends.' The option 'with' does not fit grammatically or idiomatically in this context. Therefore, the correct answer is 'C' (away).

The correct preposition to complete the phrase 'heir _____ the throne' is 'to'. The phrase 'heir to the throne' is a standard English collocation indicating the person next in line for the throne.

The correct preposition to complete the phrase is 'over,' as in 'He got over his illness,' which means he recovered from it. The other options do not fit idiomatically in this context.

The correct preposition to use with 'congratulate' when referring to an achievement is 'on'. Hence, 'We congratulate you on your achievement.' is correct.

The correct preposition to use with 'succeeded' when indicating the achievement of an action is 'in'. The phrase 'succeeded in killing the tiger' is the proper and idiomatic expression. The options 'by', 'with', and 'on' are not used with 'succeeded' in this context. Therefore, the correct answer is 'D' (in).

The word 'vestige' means a trace or remnant of something that is disappearing or no longer exists, making 'trace' the correct synonym.

The word "intractable" means difficult to manage or control, so the synonym "hard to manage" is correct. The other options do not match the meaning of "intractable."

The word 'tenacity' means the quality of being persistent and determined. Among the options, 'persistence' is the correct synonym, while the others do not relate to the meaning of tenacity.

The correct preposition to use with 'covered' in this context is 'with', as in 'Head is covered with hair.' This is the standard and grammatically correct phrase.

The correct word is 'hale,' which means healthy and strong, fitting the context of being 'quite hale and hearty.' The other options are incorrect: 'hail' is a weather phenomenon, 'hell' is a place or exclamation, and 'hall' is a building or room.