Which among following definition states that the term to be defined
is correctly applied to a given case, if and only if. the performance
of specified operations in that case yields a specified result.

The correct option is Operational definition.

An operational definition is a definition that defines a term or concept in terms of the specific process, operation, or set of validation tests used to determine its presence and quantity. It specifies the actions or operations that must be performed to measure or identify the concept.

According to this definition, a term is correctly applied to a given case if and only if performing specified operations yields a specified, measurable result. For example, defining "weight" operationally would mean stating that weight is the number that appears when an object is placed on a calibrated spring scale (the operation of placing it on the scale yields the specified result of the reading).

Let's briefly look at the other options to understand why they do not fit the description:
- Synonymous definition defines a word by providing another word that has the same or very similar meaning (e.g., defining "physician" as "doctor").
- Ostensive definition defines a term by pointing to, showing, or displaying examples of the object or concept being defined (e.g., pointing to a red apple to define the color "red").
- Quasi-ostensive definition relies on pointing to or showing an object but accompanies it with a verbal description or context to clarify which aspect of the object is being referred to.

Therefore, only the operational definition describes applying a term based on the execution of specified operations yielding a specified result.