Explanation:

Both matters prior to appointment

• Article 16(1) states that there shall be equal opportunity for the citizens in the matter of employment or appointment to any office under the State. The provision of equality is only applicable to the employment or offices which are held by the State. The State is still free to lay down the requisite qualifications for the recruitment of employees for the Government services. The Government can also pick and choose applicants for the purpose of employment as long as the applicants have been given an equal opportunity to apply for the Government service.
• Article 16(1) and (2) lay down provisions for equal opportunity of employment in the public sector. However, it is stated in clause 3 of Article 16 that nothing in this article shall prevent Parliament from making any law which prescribes to the citizens who are appointed to any office under the State in regard to any requirements as to residence within that State or Union territory prior to employment or appointment to any office under the State.

Hence option 3rd is correct statement.