The President of India is responsible for appointing several important positions in the country. Option 1, Governors of States are indeed appointed by the President. Option 2, the Chief Justice and Judges of High Court are also appointed by the President, giving them the power to administer justice at the state level. Option 4, the Chief Justice and Judges of the Supreme Court, are appointed by the President as well. However, option 3, the Vice-President, is not appointed by the President. The Vice-President is elected through an indirect election process, where members of both houses of Parliament cast their votes. Therefore, the correct answer is option 3, as the Vice-President is not appointed by the President of India.