Sentence Correction

First problem with sentence is use of 'they' there are 3 nouns which can they refer to.
so A,B,C out

this is not the actual problem with that pronoun -- remember that pronoun ambiguity is not even necessarily a problem (it is often present in the correct answers -- see a more complete explanation here: https://www.beatthegmat.com/pronoun-ambi ... tml#305959)

the real problem with the pronoun "they", in the choices that contain that pronoun, is that it doesn't stand for ANYTHING!
it's clear from the meaning of the sentence that the intended antecedent is "students" -- but the word "students" is not actually contained anywhere in those three choices. ("student activity fees" is in all three of those choices, and "students' objections" is also in the first choice -- but none of them actually say "students".)
so that's a genuine, indisputable pronoun error; those three choices are definitely gone.

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problems with (e):

* the "even though" clause creates a meaning that doesn't really make sense; the meaning created by that construction is, basically, "even though (random, unspecified) students object to particular activities, the universities can still collect activity fees."
this sentence is way too vague -- it doesn't actually come out and state the important relationship, which is the collection of scenes from the students who actually object to the activities in question.
with a little common sense, of course, people could connect the dots if they read the statement in choice (d) -- but that's not good enough; in sentence correction, the sentences need to say, EXPLICITLY, pretty much exactly what they are supposed to say.

* "have an objection" is inferior to "object". i don't know if i would go so far as to state that "have an objection" is incorrect, but, given a head-to-head choice between those two, there is no doubt that "object" is better. you

* "be" is incorrect; there is no subjunctive construction in the sentence.
i.e., you have an incorrect parallelism set up between a normal verb "may collect" and an attempted subjunctive verb "be chosen":
the supreme court has ruled that public universities may collect ... but the groups be chosen ...
nope.
by the way, the left-hand part of the sentence proves that this isn't supposed to be a subjunctive construction; since that isn't underlined, it serves as conclusive proof that the non-subjunctive form is the one you want.

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re: Passive Voice

* first, there is no issue here regarding the passive voice; all five choices in this problem use the passive voice (will be chosen / are chosen / to be chosen / are chosen / be chosen).

* second, the passive voice is not an error! this is a huge misconception that keeps popping up everywhere.