Which of the following two constructions is correct? and why?
- Some of the important aims of the UNO are to promote peace and protect human rights.
- Some of the important aims of the UNO are promoting peace and protecting human rights.
Both are acceptable. Some sounds just a bit odd to me in both: when it’s followed by a list of the ‘some things’, as it is here, I expect to find more than two items in the list. I’d prefer two here. I’d also insert another to in the first version to make the two named goals clearly two things and not one compound thing:
Since others have raised the question: I see nothing wrong with aims in this context, but goals is perhaps a little less informal; objectives verges on being jargon. Purposes is fine but has a slightly different meaning from aims.
It is always a good practice to use Objectives instead of Aims.
Your First sentence is correct
Some of the important aims of the UNO are to promote peace and protect human rights
Normally both are acceptable... When you ask "What are your hobbies? you may answer "They are to read, to swim..." or " They are reading, swimming..." you can say both here "To know you is to love you" "Knowing you is loving you" Only there is one point.. It is said that gerund/Ving form is acceptible everywhere but if there is a particular situation to+infinitive is acceptable and you can not use it for general actions..like: to smoke is bad for you but not to smoke is bad for you...It seems to me that nobody cares but this was a rule. I remember my teacher forcing us to learn this :)
but if you use this as a verb here ...you should prefer present perfect continuous..