Should we use "the" when there is a post-modification( the+noun of+noun)?

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Which one of these are correct, why and what are the nuances?

1a) This is a time of crisis

or

1b) This is the time of crisis.

2a) I was in a web of troubles.

or

2b) I was in the web of troubles.

3a) Some people have a tendency to curse when they are annoyed.

or

3b)Some people have the tendency to curse when they are annoyed.