Step 1: State the concept.
Release kinetics describe how fast a drug leaves its dosage form. Zero order means a constant amount released per unit time, independent of remaining drug concentration. First order means the rate is proportional to the amount of drug still present.
Step 2: Understand the design.
Coating granules with a water-insoluble but permeable polymer (for example ethylcellulose) creates a rate-controlling membrane. The drug must diffuse across this fixed membrane to be released.
Step 3: Reason about the kinetics.
When a saturated drug core supplies a constant driving concentration across an unchanging membrane, the diffusion rate stays nearly constant. A constant rate over time is, by definition, zero order release.
Step 4: Eliminate first and pseudo-first order.
Options 2 (first order) and 4 (pseudo first order) both imply a rate that falls as drug depletes, which is the behaviour of an uncoated, freely dissolving system, not a membrane-controlled one.
Step 5: Eliminate half order.
Option 3 (half order) is an uncommon kinetic profile not associated with simple insoluble polymer coatings, so it is discarded.
Step 6: Conclude.
A water-insoluble polymer membrane gives a constant, concentration-independent release, which is zero order, option 1.
\[ \boxed{\text{Option 1: Zero order rate}} \]