majority of

Majority of students… or The majority of steudents…
Which one is correct?
thanks in advance.

You usually need the article. More context would be useful.

the context is that:
As we all known, the majority of students end their formal education with high school.
ps: she did not mention students before this sentence.

As we all know, the majority of students end their formal education with High School.

the longest river…
the slowest cyclist…
the greatest show…
the last of a group
the majority of a group

Beeesneees,

  1. The majority of a group end their formal education with High School.
  2. The majority of a group ends their formal education with High School.
    Which one is correct?

It’s highly unlikely that you would actually say ‘the majority of a group’
‘a group’ would be defined (students, cyclists, people, etc). If it weren’t defined, then you might say ‘the majority of the group’ in which case it would be ‘ends’.

Beeesneees,
Are these sentences correct?

  1. A hundred years make a century.
  2. Only a minority of the members is in favour.

‘Make’ is correct - it is one block of years.

‘Is’ and ‘are’ are both possible, depending on your interpretation (a singular minority or a plural number of members). I would prefer ‘are’ there.