Rearrange the following sentences to form a coherent paragraph:
1. It is a process that involves systematic and objective examination of a subject to uncover new facts or verify existing ones.
2. Research serves as a fundamental pillar of academic and scientific advancement.
3. This may be either theoretical, intended to broaden knowledge, or applied, designed to address a practical problem.
4. The results of this investigation are then recorded and peer-reviewed to ensure validity and credibility.

The correct option is 2, 1, 3, 4.

Let's analyze the given sentences step-by-step to form a coherent paragraph:

Step 1: Identify the introductory sentence (Topic Sentence)
Sentence 2 ("Research serves as a fundamental pillar of academic and scientific advancement.") introduces the main subject—Research—and sets the context for the entire paragraph. Therefore, sentence 2 is the ideal starting point.

Step 2: Follow up with a definition or explanation of the process
Sentence 1 ("It is a process that involves systematic and objective examination of a subject to uncover new facts or verify existing ones.") begins with the pronoun "It", referring back to "Research" mentioned in sentence 2. It defines what research is and how it functions. Thus, sentence 1 logically follows sentence 2.

Step 3: Detail the types or classification of the process
Sentence 3 ("This may be either theoretical, intended to broaden knowledge, or applied, designed to address a practical problem.") uses the demonstrative pronoun "This" to refer to the process/examination introduced in sentence 1. It further categorizes research into theoretical or applied forms. Thus, sentence 3 logically follows sentence 1.

Step 4: Provide the concluding statement
Sentence 4 ("The results of this investigation are then recorded and peer-reviewed to ensure validity and credibility.") brings the logical sequence to a conclusion by describing what happens with the results obtained from the research investigation. The word "then" indicates a final sequential step. Thus, sentence 4 logically completes the paragraph.

Combining these steps, the logical order of sentences is 2, 1, 3, 4.