The correct answer is option 1, which states that the "overthrow of alien rule" is not a political method of the moderates in the National Movement.

To better understand this, let`s dissect the other options:

- Option 2: "Constitutional agitation" refers to the idea of using peaceful and legal means to bring about political change. The moderates believed in advocating for their rights and demands through constitutional methods such as public meetings, petitions, and discussions with the British government.

- Option 3: "Slow, orderly political progress" suggests that the moderates favored a gradual and organized approach to achieving political reforms. They believed in working within the existing framework of the British administration and using dialogue rather than confrontation.

- Option 4: "Mobilisation of public opinion" indicates that the moderates focused on raising awareness and garnering support from the general public. This involved organizing political meetings, public speeches, and publishing articles and pamphlets to gain public sympathy and support for their cause.

In contrast, the "overthrow of alien rule" implies a more radical and violent approach to bringing about political change, which was not in line with the moderate`s ideology. Therefore, option 1 is the correct answer as it is not a political method