Which of the following sentences is correct?

The correct answer is Option (2) → From the walls of the old fort at Srirangapatna, we could see the Kaveri flowing past.

“The” before the names of rivers:

• The name of a river always takes the before it.
• The Kaveri is a river, so we say the Kaveri.

Why the Other Options are Incorrect?

Option 1: My cousin brother from Lucknow is coming to stay with us for the Dussehra holidays. — Incorrect. “Cousin” already means the child of an uncle or aunt. Adding “brother” says the same thing twice.
Corrected: My cousin from Lucknow is coming to stay with us for the Dussehra holidays.

Option 3: Many a passenger have missed this train because of the confusing platform numbers. — Incorrect. “Many a” is followed by a singular noun and a singular verb.
Corrected: Many a passenger has missed this train because of the confusing platform numbers.

Option 4: Both the bus driver as well as the conductor got down to help the old man with his bags. — Incorrect. “Both” is always paired with “and”, not with “as well as”.
Corrected: Both the bus driver and the conductor got down to help the old man with his bags.