The correct answer is option 4, Parliament by law. In India, the salaries and allowances for Members of Parliament (MPs) are determined by Parliament itself through legislation. This means that the Parliament of India, which consists of both the Lok Sabha (House of the People) and the Rajya Sabha (Council of States), has the authority to pass laws regarding the salaries and allowances of MPs.

The Union Cabinet, option 1, refers to the group of ministers who are chosen by the Prime Minister to assist in the administration and decision-making in the central government. While the Union Cabinet may have influence over various policies and decisions, including those related to MPs, they do not have the exclusive authority to determine the salaries and allowances of MPs.

The Ministry of Parliamentary Affairs, option 2, is responsible for coordinating and facilitating the legislative business in Parliament. While they may provide recommendations or input regarding MPs` salaries and allowances, the final decision-making authority lies with Parliament itself.

Similarly, the Cabinet Secretariat, option 3, acts as a secretariat for the Union Cabinet and facilitates its functioning. They do not have the direct authority to determine MPs` salaries and allowances.

Therefore, the correct answer is option 4, Parliament by law.