From the following options, choose the most suitable form of the word…

The correct answer is Option (2) → fell

Fell and fall:

• Fell (fell, felled, felled) is a transitive verb meaning to cut down a tree; it takes an object.
• Fall (fall, fell, fallen) is intransitive: a tree falls by itself, but nobody can "fall a tree".
• This sentence: after "allowed to", the base form is needed, and the trees are the object, so the verb is to fell the trees.
• Complete sentence: Nobody is allowed to fell the trees in the protected areas of Nagarjuna forest.
  Example: The workers had to fell the dead tree before it crashed onto the road.

Why the Other Options are Incorrect?

Option 1: fall — Incorrect. Fall means to drop down by itself and takes no object, so "to fall the trees" is wrong.
Example: The old tree may fall in the storm.

Option 3: fallen — Incorrect. Fallen is the past participle of fall; it cannot follow "to" here.
Example: Several branches had fallen overnight.

Option 4: have fall — Incorrect. "Have" needs a past participle (have fallen), so "have fall" is ungrammatical; it would also give the wrong verb.
Example: The leaves have fallen from the trees.

Contrast: fell (cut down) takes an object: workers fell a tree; fall takes none: a tree falls.