A developer writes a Lightning web component that displays a dropdown list of all custom...

Comprehensive and Detailed Explanation:

To programmatically identify custom objects in Apex, developers utilize Schema Describe information. The Schema.getGlobalDescribe() method returns a map of all object tokens in the org. By iterating through these tokens and calling the getDescribe() method on each, the developer can access various properties of the object's metadata.

The specific property to distinguish between standard and custom objects is the isCustom() method (Option C). This boolean method returns true if the object is a custom object (including custom settings and custom metadata types) and false if it is a standard platform object.

Option A is incorrect because @salesforce/schema is used in LWC to import references to specific known objects/fields, not to discover the entire org's metadata dynamically. Option B is incorrect as getObjectType() returns an SObjectType token, not a string value like 'Custom'. Option D is incorrect because there is no getCustomObjects() method in the standard Schema class; discovery must be done via the global describe map.