Fill in the blank choosing the appropriate word from the options give…

The correct answer is Option (4) → oldest

Superlative degree:

• When one thing is compared with all the others in a group, the adjective takes the superlative degree, usually with the.
• "Old" has two sets of forms:
  • old – older – oldest: for people and things in general;
  • old – elder – eldest: only for members of the same family.
• This sentence: "the" before the blank and "in the city" compare this college with every college in the city, so oldest is needed.
  Example: This is the oldest temple in the town.

Complete sentence: This is the oldest college in the city.

Why the Other Options are Incorrect?

Option 1: old — Incorrect. Old is the positive degree; "the old college in the city" makes no comparison with the other colleges.
Example: This is an old college.

Option 2: older — Incorrect. Older is the comparative degree, used for two things with "than".
Example: This college is older than that one.

Option 3: eldest — Incorrect. Eldest is used only for members of a family, not for a college.
Example: My eldest brother lives in Pune.