The most likely factory responsible for lowering the pH of the river water is (b) Lead battery manufacturing factory.
Explanation: Lead batteries contain sulfuric acid, which is highly acidic and when released into the river can significantly lower the pH.
Why other options are incorrect:
(a) Soap and detergent factory:
Soap and detergents are typically alkaline (meaning they have a high pH), not acidic.
(c) Plastic cup manufacturing factory:
Plastics are generally neutral or slightly alkaline. While some plastics might use chemicals during production, these are usually contained within the plastic and not released into the effluent.
(d) Alcohol distillery:
Although some alcohols can be acidic, the effluents from distilleries are more likely to be slightly alkaline due to the presence of organic compounds, not strong acids like sulfuric acid.