Yes, you can apply for vacancies in both public sector and private sector banks through the IBPS Clerk Exam.

IBPS Clerk Exam
The Institute of Banking Personnel Selection (IBPS) conducts the IBPS Clerk Exam to recruit candidates for clerical positions in various banks in India. The exam is held in two stages: Preliminary Exam and Main Exam. Candidates who clear both stages are eligible for vacancies in both public sector and private sector banks.

Vacancies in Public Sector Banks
Public sector banks include nationalized banks such as State Bank of India (SBI), Punjab National Bank (PNB), Bank of Baroda, etc. These banks are owned by the government and provide banking services to the public. They offer a wide range of career opportunities and have a large network of branches across the country. Through the IBPS Clerk Exam, you can apply for vacancies in these public sector banks.

Vacancies in Private Sector Banks
Private sector banks, on the other hand, are owned by private individuals or corporations. Examples of private sector banks in India are ICICI Bank, HDFC Bank, Axis Bank, etc. These banks also provide banking services to the public but have a different ownership structure. Through the IBPS Clerk Exam, you can also apply for vacancies in private sector banks.

Common Eligibility Criteria
The eligibility criteria for both public sector and private sector banks are the same for the IBPS Clerk Exam. Candidates must have a minimum educational qualification of a Bachelor's degree from a recognized university. They must also be within the age limit specified by IBPS.

Application Process
To apply for vacancies in both public sector and private sector banks, candidates need to fill out the online application form for the IBPS Clerk Exam. The application form requires personal and educational details, and candidates must also upload scanned copies of their photograph and signature. After successfully submitting the application form and paying the application fee, candidates can choose the banks they wish to apply for.

Conclusion
In conclusion, the IBPS Clerk Exam provides an opportunity for candidates to apply for vacancies in both public sector and private sector banks. The exam follows a common eligibility criteria for both types of banks, and candidates can choose their preferred banks during the application process.