Public nuisance, as the principle defines it, turns on effect rather than on intent, ownership of the land, or personal gain. The test is whether the act causes, or is likely to cause, common injury, danger or annoyance to the public, and the principle goes further by saying even some advantage from the act does not excuse it.
Here, the smoke from A's stubble burning does not stay confined to his own fields, it spreads over the adjoining public road that people use to travel and drifts into houses in the nearby residential colony. That spread to a road and multiple homes is precisely a common annoyance affecting the public rather than any single individual.
None of the usual defences work against that test, not having named a specific victim, not personally profiting from the neighbours, owning the land where the fire was lit, or lacking any intent to harm, since the principle's own wording strips each of those away as a valid excuse for a nuisance that in fact reaches the public.
So the correct answer is A has committed public nuisance.
Asking what fact would need to be different for each option to hold shows exactly where three of the choices fail.
Since the smoke's actual reach into public areas is already established and none of the three alternative conditions are what the principle actually tests, public nuisance is the option that needs no unstated fact to be true.
Therefore, the correct answer is A has committed public nuisance.