Which of the following administration routes involves delivering medication through mucous membranes?

The route that involves delivering medication through mucous membranes is the buccal route. When medications are administered buccally, they are placed between the gums and the inner lining of the cheek, where they can dissolve and be absorbed directly into the bloodstream through the mucous membranes. This method allows for rapid absorption and avoids first-pass metabolism in the liver, making it an effective delivery system for certain medications.

Other administration routes, such as subcutaneous, intravenous, and intramuscular, do not involve mucous membranes. Subcutaneous injections deliver medication into the fatty tissue just under the skin, intravenous injections deliver medications directly into the bloodstream through a vein, and intramuscular injections involve administering medication deep into muscle tissue. Each of these routes has its specific indications and absorption characteristics but does not utilize mucous membranes for the delivery of medications.