Step 1: Understanding the Question:
We need to rearrange the given fragments to construct a coherent, grammatically correct sentence.
Step 2: Key Formulas and approach:
1. Find the main subject of the sentence, which is often a noun phrase.
2. Check for participle modifiers (present or past participles) that describe the noun phrase.
3. Ensure the singular verb "is" agrees with the singular noun phrase head "the number".
Step 3: Detailed Explanation:
$\bullet$ Fragment S: "the number of students" is the logical starting subject. Remember that "the number of" is grammatically singular and takes a singular verb.
$\bullet$ This subject is modified by the active participle phrase in Fragment P: "applying for masters in foreign universities". This gives S $\rightarrow$ P.
$\bullet$ Now we need the main verb of the sentence. Fragment R: "is increasing significantly" has the singular verb "is", which matches the singular head "the number". This gives S $\rightarrow$ P $\rightarrow$ R.
$\bullet$ Lastly, the reason for this increase is provided in Fragment Q: "due to better opportunities". This completes the sentence, giving S $\rightarrow$ P $\rightarrow$ R $\rightarrow$ Q.
Step 4: Final Answer:
The logical sequence is SPRQ, which is Option (C).