Choose the grammatically correct sentence:

The correct answer is Option (2) → Our class monitor requested an extra fan from the principal during the summer exams.

“Request” takes its object directly:

• The verb “request” is followed directly by the thing asked for, with no “for” after it: “requested an extra fan”.

Why the Other Options are Incorrect?

Option 1: This letter was wrote by my grandfather when he was posted in Assam. — Incorrect. A passive verb is “was” + the past participle (V3). The V3 of “write” is “written”, not “wrote”.
Corrected: This letter was written by my grandfather when he was posted in Assam.

Option 3: My little sister prefers idli than dosa for breakfast. — Incorrect. “Prefer” is followed by “to”, not “than”, when two things are compared.
Corrected: My little sister prefers idli to dosa for breakfast.

Option 4: Each of the buses on this route have a GPS tracker now. — Incorrect. With “each of”, the subject is “each”, which is singular. So the verb must be singular.
Corrected: Each of the buses on this route has a GPS tracker now.