The correct answer is option 1 only.

Statement 1 is correct. Article 77(3) of the Indian Constitution empowers the President to make rules for the more convenient transaction of the business of the Government of India and for the allocation among Ministers of the said business. These rules, known as the Government of India (Allocation of Business) Rules, 1961, define the distribution of business among the various ministries and departments of the Government of India.

Statement 2 is incorrect. While the Prime Minister is the head of the government and exercises significant executive powers, all executive actions of the government are not expressed to be taken in his name. Executive actions can be taken by various authorities and officials under the Constitution and other laws.