The interior minister explained that one of the village planning

adkikani , you are correct. "Characteristics" is the object of a preposition. The object of a preposition cannot be the subject of the sentence.

[Disclaimer: although the object of a preposition cannot be the subject of a sentence, in one rare case, a whole noun phrase is the subject, and it includes the object of a preposition: subgroup modifiers such as some of whom, all of which, etc.)

• C is correct because "one of the Xs" is singular, based on the rule below. C's verb, WAS, is singular.

• Summary of the rule
I would memorize this rule . . . or understand why it works. Or both.

When we see one of the Xs, whether it is singular or plural turns on whether the phrase is accompanied by THAT/WHO.

ONE OF THE Xs

ONE OF THE Xs + that/who + VERB = always plural

ONE OF THE Xs + VERB = always singular

Look for the words that or who after "one of the Xs."

If that or who IS present, then one of the Xs is plural.
→ She is one of the students who learn Spanish and English simultaneously.
If that or who is NOT present, then one of the Xs is singular.
→ One of the students learns Spanish and English simultaneously.

Explanation of the rule

If we think about it in context, those two rules make sense.
-- In the first case, the person is the only one [of the Xs] who does [singular] Y. Only one X does Y.
-- In the second case, the person is not the only one who does Y.
The person is one of the many Xs who do [plural] Y. Many Xs do Y.

In American football, the quarterback Colin Kaepernick took a knee to protest injustice in 2016. Other players and coaches followed. Soon a culture war ensued between Donald Trump and the players who protested or showed solidarity. The NFL banned the practice this year.

Singular - "one of the Xs" VERBS
One of the athletes [Colin Kaepernick] protests injustice by taking a knee.

Meaning: He is the only athlete who chooses "taking a knee" to protest injustice.
-- Other athletes do not protest by "taking a knee."
-- Other athletes protest in different ways. Some of the athletes wear colored ribbons.
Some athletes remain in the locker room until game time.
Other athletes raise clenched fists (and are stripped of gold and silver medals).
-- Only THIS athlete is known to protest in this way.
• In the singular case in which only THE is used (without WHO or THAT), no other Xs do this action.
Only one of the Xs does this action.
(singular) One . . .protests (singular)

• In the plural case with THAT or WHO, there are many Xs who do this action.

Plural - "one of the Xs" that/who VERB

He is one of the athletes WHO protest injustice by taking a knee.

Meaning: There are many athletes who protest by taking a knee.
-- There is a group of athletes who all protest by taking a knee, and he is one of (he is part of) that group.
He is one of many who protest in that way.
(plural) athletes . . . protest

So, adkikani , in correctly deciding that the object of a preposition could not be the subject of the sentence, you got to the correct conclusion: the subject is singular.

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workout , maybe I am missing something you intend, but . . . As you note, the prepositional phrase can affect the subject and hence determine whether the verb should be singular our plural.

I agree that the prepositional phrase modifies the subject -- but the subject in the example used is "some," not "students."

In other words, the object of the preposition (students) is not the subject of the sentence. I think what I see may be a typo.

thangvietnam , E is utter nonsense.
Answer E is indeed missing a "that."
If you read the thread, you will see that others have already discussed other problems with Answer E.
If you have any specific questions about E, please let us know!

*****

adkikani , I hope that helps.