Read the passage.
from War and Peace
Prince Vasili always spoke languidly, like an actor repeating a stale part. Anna Pavlovna Scherer on the contrary, despite her forty years,
overflowed with animation and impulsiveness. To be an enthusiast had become her social vocation and, sometimes even when she did not feel like
it, she became enthusiastic in order not to disappoint the expectations of those who knew her. The subdued smile which, though it did not suit her
faded features, always played round her lips expressed, as in a spoiled child, a continual consciousness of her charming defect, which she neither
wished, nor could, nor considered it necessary, to correct.
(from War and Peace by Leo Tolstoy)
Which is the best definition of languidly"?
1. carefully
O 2 infrequently
03. listlessly
4. soothingly

From this excerpt, it is clear that Prince Vasili's character was completely contrary to Anna Pavlovna's. She was impulsive, active, full of energy, joy and laughter. She constantly expressed her vitality and enjoyed in social interactions.

Now, it comes natural to define languid as completely opposite to this. Thus, languidly depicts doing something in a manner that lacks vitality, energy, speed or interest; doing something slowly, lazily, deprived of every effort and motive.

Although all the given answers could, more or less, be regarded as partial synonyms for "languidly", "carefully" and "soothingly" are usually seen as positive qualities, while "infrequently" simply means "rarely", which leaves us with "listlessly" as the best fitting answer.