The object of the Butler Committee of 1927 was to improve the relationship between the Government of India and the Indian States. Option 4 is therefore the correct answer.

The Butler Committee was officially known as the Indian States Committee and was appointed by the British Government in 1927 under the chairmanship of Sir Harcourt Butler. Its main objective was to review the relationship between the Government of India and the Indian States, which were semi-autonomous territories ruled by native princes and under the suzerainty of the British Crown.

The Committee was formed in response to growing demands from the Indian nationalist movement for greater self-rule and autonomy. The British Government recognized that the relationship between the Indian States and the British Indian Government needed to be re-examined to ensure stability and to prevent any future political unrest.

The Butler Committee was tasked with examining the constitutional position of the Indian States, their relationship with the British Crown and the Government of India, and their overall contribution to the development of India. The Committee submitted its report in 1929, which contained several recommendations that aimed to strengthen the relationship between the Indian States and the British Indian Government.

Some of the key recommendations of the Butler Committee included the establishment of a federal system of government for India, with the Indian States having representation in a central legislative body. The Committee also recommended the creation of a council of princes to provide a forum for the Indian princes to discuss matters of mutual interest.

The Butler Committee`s recommendations played an important role in shaping the Government of India Act of 1935, which introduced several reforms that gave Indian provinces greater autonomy and paved the way for India`s eventual independence in 1947.

In conclusion, the Butler Committee of 1927 was formed to improve the relationship between the Government of India and the Indian States. Its recommendations aimed to create a more federal and inclusive system of government that would better represent the interests of all Indians.