The correct option is 2 and 3 only.
Explanation
The removal of the President of India is governed by the process of impeachment under Article 61 of the Constitution. It is a quasi-judicial procedure conducted by the Parliament.
Statement 1 is Incorrect.
The President is not removed by the Supreme Court. The power to impeach and remove the President is vested exclusively in the Parliament. While the Supreme Court has the authority to inquire into disputes regarding the election of the President (Article 71), the inquiry during impeachment is conducted by the House of Parliament investigating the charges (or a body appointed by it).
Statement 2 is Correct.
According to Article 61(1), the President can be impeached only on the ground of "violation of the Constitution". The Constitution does not define the specific meaning or scope of this phrase, but it remains the sole constitutional ground for removal.
Statement 3 is Correct.
The impeachment process requires a very strict special majority. The resolution must be passed by a majority of not less than two-thirds of the total membership of each House of Parliament. This is the highest majority threshold prescribed in the Indian Constitution.
Key Takeaway:
The President can be impeached solely for the "violation of the Constitution" through a Parliamentary resolution passed by a majority of two-thirds of the total membership of both Houses.