Step 1: Define pseudo first order reaction.
A pseudo first order reaction is a reaction which is actually of higher order but appears to follow first order kinetics because one of the reactants is present in large excess and its concentration remains nearly constant.
Step 2: Analyze option (A).
In the hydrolysis of methyl acetate, water is taken in large excess. Due to this, the concentration of water remains constant throughout the reaction. Hence, the rate depends only on the concentration of methyl acetate, making it appear as a first order reaction.
Step 3: Analyze other options.
(B) Decomposition of $N_2O_5$ is a true first order reaction.
(C) Isomerization of cyclopropane is also a true first order reaction.
(D) Decomposition of hydrogen peroxide is not pseudo first order in nature.
Step 4: Conclusion.
The hydrolysis of methyl acetate is a classic example of a pseudo first order reaction.