When U load the data into a table in Utility mode,all the constraints are disabled and then data is loaded which leads to faster access.

During API Mode constraints will be enables so that the access will be slow.

API and UTILITY are the two possible interfaces to connect to the databases to perform certain user specific tasks. These interfaces allows the user to access or use certain functions (provided by the database vendor) to perform operation on the databases.The functionality of each of these interfaces depends on the databases.

API has more flexibility but often considered as a slower process as compared to UTILITY mode. Well the trade off is their performance and usage.

I think you've the misunderstanding.  Using utility mode does not need to disable constraints nor indexes, if you use the conventional path load (say Oracle).

For direct path, you might need to.

Basically, api mode is using oci calls, so it is much slower.

utility mode is calling the database client utility, e.g. Oracle sqlldr.