I am not a teacher.
I think the first one would be acceptable to some people, but I would change it.
"This year more students passed the exam than did last year."
The second one is wrong as it stands. You can say "than they did..." if you change the beginning, "Nowadays, people use beepers less than they did in the past."
Otherwise, "Nowadays fewer people use beepers than did in the past."
The last two are grammatically OK.
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