Which of the following sentences is correct?

The correct answer is Option (4) → Do you know whose umbrella is lying on the bench outside the staff room?

“Whose” to ask about the owner:

• “Whose” asks or tells who owns something.
• The sentence asks who owns the umbrella, so whose umbrella is correct.

Why the Other Options are Incorrect?

Option 1: Rohan’s sister is a six-years-old girl who already reads Hindi comics on her own. — Incorrect. When a number and a noun are joined to describe another noun, the noun stays singular.
Corrected: Rohan’s sister is a six-year-old girl who already reads Hindi comics on her own.

Option 2: We have visited the Salar Jung Museum during our trip to Hyderabad last December. — Incorrect. “Last December” is a finished past time, so it takes the simple past, not “have visited”.
Corrected: We visited the Salar Jung Museum during our trip to Hyderabad last December.

Option 3: The nurse which gave me the injection at the clinic was very gentle. — Incorrect. “Which” is used for things. For a person, we use “who”.
Corrected: The nurse who gave me the injection at the clinic was very gentle.