The choice between individual entrance exams for each state versus a single centralized exam depends on various factors, including the goals of the education system, regional diversity, and the need for standardization. Here are some considerations for each approach:

Centralized Exam
Advantages:

Standardization: Ensures a uniform measure of knowledge and skills across all states, providing a consistent benchmark for comparing students.
Fairness: Reduces disparities between states in terms of testing quality and resources, offering all students an equal opportunity.
Efficiency: Streamlines the process, potentially reducing administrative costs and complexity by having a single exam.
Mobility: Easier for students who move between states, as they face the same exam regardless of location.
Disadvantages:

One-Size-Fits-All: May not account for regional educational differences or specific needs, potentially disadvantaging students in areas with different curricula or learning environments.
High-Stakes Pressure: A single exam can place significant pressure on students, potentially impacting their mental health and performance.
Logistical Challenges: Coordinating a nationwide exam can be complex and require substantial resources.
Individual State Exams
Advantages:

Regional Relevance: Allows for exams to be tailored to reflect regional curricula, educational standards, and local contexts, which may be more relevant for students.
Flexibility: States can adjust exams to address specific educational priorities and needs, potentially improving the alignment between teaching and assessment.
Reduced Pressure: Students may face less pressure compared to a high-stakes, nationwide exam, as the stakes are limited to their state context.
Disadvantages:

Variability: Different states may have varying standards and difficulty levels, making it harder to compare student performance nationally.
Inequality: Disparities between states in terms of resources and exam quality can lead to unequal opportunities and outcomes for students.
Administrative Complexity: Managing and coordinating multiple exams can increase administrative burdens and costs.
Hybrid Approach
A hybrid approach, combining elements of both systems, might address some of these concerns:

State-Specific and National Sections: States could have exams tailored to regional curricula with a standardized section for core subjects.
Benchmark Assessments: A centralized exam could be used for benchmarking purposes, supplemented by state-specific assessments to capture regional variations.
Ultimately, the choice depends on the educational goals and context of the region. Balancing standardization with regional relevance and fairness is key to designing an effective entrance exam system.