The correct option is "Neither 1 nor 2" because the Legislative Council of a State in India cannot exceed one-third of the size of the Legislative Assembly, not half, as stated in the first statement. Additionally, while the Governor does appoint the Chairman of the Legislative Council, it is important to note that the Chairman is typically the Deputy Chairman of the Council, elected by its members, which makes the second statement misleading. These nuances are essential for understanding the structure and functioning of the Indian parliamentary system as covered in standard UPSC-level study materials.