Step 1: Understanding the Concept:
This question tests Subject-Verb Agreement, specifically the use of indefinite pronouns as subjects.
When a sentence begins with "Each of," the word "Each" is the subject, and it is grammatically singular.
Step 2: Detailed Explanation:
Let's analyze the sentence structure:
$[Each] + [of the players] + [have performed...]$
1. The Singular Subject Rule:
The word "Each" refers to every individual member of a group considered separately. Because it refers to individuals {one at a time}, it is always singular.
Many students make the mistake of looking at "players" (which is plural) and choosing a plural verb. However, "players" is merely the object of the preposition "of."
2. Matching the Verb:
- Subject: Each (Singular)
- Required Verb: Singular
In the Present Perfect tense, the singular auxiliary is "has," and the plural is "have."
3. Evaluating the Options:
- Option (A) has performed: This is the singular form of the verb. It correctly agrees with "Each." This is the best replacement.
- Option (B) were performing: This is plural past continuous. It is wrong because it's plural and it changes the tense from perfect to continuous.
- Option (C) perform: This is the plural present tense. Wrong because "Each" needs "performs" (singular).
- Option (D) have been performing: This is the plural present perfect continuous. It is wrong because of the plural auxiliary "have."
Example for comparison:
- {Correct:} Each of the students has a book.
- {Incorrect:} Each of the students have a book.
Step 3: Final Answer:
Because "Each" acts as a singular subject, it must be followed by "has performed." Thus, Option (A) is the correct answer.