1. You should study hard to get into university.

2. You should study hard to go into university.

3. You should study hard to go to university.

4. You should study hard to get to university.

5. You should study hard to enter university.

(Are all the same in meaning? Which ones are popular?)

They are all the same.

But numbers 1 and 3 are most commonly used.

One difference between British English and American English is that Americans use "the" before university.

Example: You should study hard to get into the university.

But your sentences are more common in the United Kingdom.

All of the sentences you provided have similar meanings, but there are slight differences in the prepositions being used. Let's analyze each sentence:

1. "You should study hard to get into university."
This sentence suggests that studying hard is necessary in order to gain admission or be accepted into a university.

2. "You should study hard to go into university."
In this sentence, "go into" implies the act of entering or starting university. It can be interpreted as studying hard to begin your journey in a university.

3. "You should study hard to go to university."
Similar to the previous sentence, "go to" implies the act of attending or being a student at a university. This sentence indicates that studying hard is important for becoming a university student.

4. "You should study hard to get to university."
Using "get to" implies reaching the point of attending a university, suggesting that studying hard is necessary to achieve that goal.

5. "You should study hard to enter university."
This sentence conveys that studying hard is essential for successfully gaining admission to a university.

In terms of popularity, all of these sentences are commonly used, and the choice between them often depends on regional preference or individual style. Generally, sentences 1, 3, and 5 ("get into," "go to," and "enter") are more commonly used, while sentences 2 and 4 ("go into" and "get to") may be less frequently heard.