Statement Analysis:
The question asks about the appointment and removal process of the chairpersons of the National Human Rights Commission (NHRC) and State Human Rights Commission (SHRC). Let's analyze each statement:

Statement 1: Chairpersons of the NHRC and SHRC are appointed by the President of India.
Statement 2: Only the President of India can remove the chairpersons of NHRC and SHRC.

Explanation:
Statement 1:
The first statement is incorrect. The chairpersons of the NHRC and SHRC are not appointed by the President of India. The appointment process differs for both commissions.

- National Human Rights Commission (NHRC): The chairperson of the NHRC is appointed by the President of India on the recommendation of a committee consisting of the Prime Minister as the Chairperson, the Speaker of the Lok Sabha, the Deputy Chairman of the Rajya Sabha, the leaders of the opposition in both the Houses of Parliament, the Minister in charge of the Ministry of Home Affairs, and the Minister of State in the Ministry of Home Affairs. Therefore, the President does not directly appoint the chairperson of the NHRC.

- State Human Rights Commission (SHRC): The chairperson of the SHRC is appointed by the Governor of the respective state on the recommendation of a committee consisting of the Chief Minister as the Chairperson, the Speaker of the Legislative Assembly, the Minister in charge of the Department of Home, the Minister in charge of the Department of Law, and the Leader of the Opposition in the Legislative Assembly. Again, the President of India does not have a direct role in the appointment of the chairperson of the SHRC.

Statement 2:
The second statement is correct. Only the President of India can remove the chairpersons of the NHRC and SHRC. The removal process is similar for both commissions.

- National Human Rights Commission (NHRC): The chairperson of the NHRC can be removed by the President of India on the grounds of proved misbehavior or incapacity. However, the President can only remove the chairperson after an inquiry, which is conducted by a Supreme Court judge appointed by the President, concludes that the chairperson should be removed.

- State Human Rights Commission (SHRC): The chairperson of the SHRC can be removed by the President of India on the same grounds after an inquiry conducted by a sitting judge of the High Court concludes that the chairperson should be removed.

Conclusion:
In conclusion, statement 1 is incorrect as the chairpersons of the NHRC and SHRC are not appointed by the President of India. However, statement 2 is correct as only the President of India can remove the chairpersons of both commissions. Therefore, the correct answer is option 'B' - 2 only.