Choose the correct modal verb to go in the gap.
'Might' is used for possibility.
'Must' is used for obligation.
This is a 3rd conditional sentence referring to the past. We use 'would' for this, not 'will'. 'Shall' doesn't fit as it's used for future intentions.
This is about obligation. You can't use 'to' with 'must' or 'should'.
This is about permission so it is 'can'.
It's about something that was not necessary.
'Should' is used for advice, and in this case the advice is not to do something. 'Shall' is used in other ways, such as for suggestions for future intentions.
'Will' is used for definite plans in the future.
We can use 'shall' for suggestions.
'Ought' is for obligation or advice. It's not quite as strong as 'must'. 'Can't' and 'must not' don't make sense here, as the person is 'tired'.