Step 1: Understand the reaction.
The hydrolysis of ethyl acetate with dilute NaOH is a simple ester hydrolysis reaction. This reaction follows a first-order rate law with respect to both the ester and NaOH.
Step 2: Analyze the options.
- 1st order (Option A) is correct as ester hydrolysis with dilute NaOH is a first-order reaction.
- 2nd order (Option B) would imply a second-order dependence, which is not the case for this reaction.
- 3rd order (Option C) is not typical for ester hydrolysis.
- Zero order (Option D) would indicate that the reaction rate does not depend on concentration, which is not true for this reaction.
Step 3: Apply to the options.
The correct answer is (A) 1.
Final Answer:
\[
\boxed{\text{1}}
\]