Which of the following lists correctly names major types of database management systems (DBMS) based on their underlying data models?

Introduction / Context:
Database management systems can be classified in many ways, but one of the most common is by the underlying data model they use. Historically, several major data models have been proposed and implemented, and these models influence how data is structured and accessed. This question asks you to identify a list that correctly names key types of DBMS based on data model rather than on performance, size, or application domain.

Given Data / Assumptions:

• The focus is on classification by data model, not by hardware platform or usage pattern.
• Classical DBMS data models include hierarchical, network, relational, and object oriented models.
• Some options list terms that do not correspond to standard DBMS types.
• We assume standard textbook taxonomy from introductory database courses.

Concept / Approach:
In DBMS theory, major data models include the hierarchical model, the network model, the relational model, and the object oriented model. Hierarchical and network models were common in early database systems, while the relational model became dominant due to its simplicity and strong mathematical foundation. Object oriented and object relational models emerged later to better handle complex data. A correct list of DBMS types should mention these well known categories and avoid unrelated mathematical terms or vague classifications.

Step-by-Step Solution:
Step 1: Recall standard DBMS classifications based on data model.Step 2: Compare each option with this standard classification.Step 3: Option A lists hierarchical, network, relational, and object oriented DBMS, which matches textbook lists.Step 4: Option B lists linear, quadratic, and exponential, which are algorithmic growth rates, not DBMS types.Step 5: Option C and D use terms that are not standard data model categories for DBMS.

Verification / Alternative check:
You can verify this by checking common database literature, where hierarchical, network, and relational models are almost always mentioned when discussing the evolution of database systems. Object oriented and object relational systems are also widely recognized. No reputable source classifies DBMS into linear, quadratic, or exponential types, nor into static and dynamic DBMS in the sense of fundamental data models. This confirms that option A is the only option consistent with established terminology.

Why Other Options Are Wrong:
Option B is incorrect because linear, quadratic, and exponential describe time complexity classes in algorithm analysis, not database models. Option C is wrong because graphical, textual, and multimedia might describe types of data but not the underlying DBMS data models. Option D is incorrect because static, dynamic, and hybrid are vague descriptors and are not used universally as primary DBMS model categories.

Common Pitfalls:
A common mistake is to confuse data types or application categories with data models. For example, a multimedia database may still use a relational or object oriented model internally. Another pitfall is to think in terms of algorithmic complexity, which belongs to data structure and algorithm courses, not to DBMS classification. Keeping the focus on structural concepts like hierarchies, networks, relations, and objects helps avoid these misunderstandings.

Final Answer:
The correct list of major DBMS types based on data model is Hierarchical, network, relational, and object oriented DBMS, which corresponds to option A.