Step 1: Understand the noun phrase.
The phrase "problems in ______________ of this plan" suggests the need for a noun that specifies the execution or implementation of the plan.
Step 2: Evaluate the options.
% Option
(1) the: Correct. "The execution" or "the implementation" is the appropriate phrase to complete the meaning.
% Option
(2) a: Incorrect. This would be grammatically incorrect because "execution" or "implementation" refers to a specific action, requiring the definite article "the."
% Option
(3) an: Incorrect. The article "an" does not fit the context.
% Option
(4) on: Incorrect. "On" does not fit the prepositional phrase structure.