Yes, you can register for the UGC NET Exam without completing your master's degree within the required time frame. The National Eligibility Test (NET) is conducted by the National Testing Agency (NTA) on behalf of the University Grants Commission (UGC) to determine the eligibility of candidates for the role of Assistant Professor and for the award of Junior Research Fellowship (JRF) in Indian universities and colleges.

Eligibility Criteria for UGC NET Exam:
To be eligible for the UGC NET Exam, candidates must fulfill certain criteria, including educational qualifications. The eligibility criteria state that candidates must have completed their master's degree or equivalent in a relevant subject with at least 55% marks (50% for reserved categories) from a recognized university or educational institution. However, there is no mention of a specific time frame within which the master's degree must be completed.

Process of Registration:
To register for the UGC NET Exam, you need to follow these steps:
1. Visit the official website of NTA NET.
2. Click on the "Apply Online" link.
3. Fill in the required personal and educational details.
4. Upload the necessary documents, such as a scanned photograph and signature.
5. Pay the application fee through the provided payment options.
6. Submit the application form.
7. Take a printout of the confirmation page for future reference.

Important Points to Consider:
- While you can register for the UGC NET Exam without completing your master's degree within the required time frame, it is important to note that you will need to complete your degree before the final selection process.
- The UGC NET Exam is conducted twice a year in various subjects, so you have multiple opportunities to appear for the exam.
- It is advisable to check the eligibility criteria specific to your chosen subject, as some subjects may have additional requirements.
- Make sure to keep track of the deadlines for registration and submission of the application form.

In conclusion, you can register for the UGC NET Exam without completing your master's degree within the required time frame. However, it is essential to complete your degree before the final selection process. Keep track of the deadlines and check the eligibility criteria specific to your chosen subject. Best of luck with your UGC NET Exam preparation!