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Solution:
'On' is used to show that something is in a position above something else and touching it. Here 'homework' will be above the surface of the 'desk' and touching it.

Solution:
We use 'at' for a precise time, 'in' for months, years, centuries and long periods and 'on' for days and dates.

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Solution:
'After' means 'later than' and 'next in time or place'. 'After' can be used before a noun phrase (as a preposition).