"Partition" here refers not only to the division of the Bengal province of British India into East Pakistan and West Bengal (India), and the similar partition of the Punjab province into Punjab (West Pakistan) and Punjab, India, but also to the respective divisions of other assets, including the British Indian Army, the Indian Civil Service, and other administrative services, the railways, and the central treasury.
The secession of Bangladesh from Pakistan in 1971 is not covered by the term Partition of India, nor is the earlier separation of Burma (now Myanmar) from the administration of British India, or the even earlier separation of Ceylon (now Sri Lanka). Ceylon was part of the Madras Presidency of British India from 1795 until 1798 when it became a separate Crown Colony of the Empire.
Burma, gradually annexed by the British from 1826-86 and governed as a part of the British Indian administration until 1937, was directly administered thereafter. Burma was granted independence on 4 January 1948 and Ceylon on 4 February 1948. (See History of Sri Lanka and History of Burma.)
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Bhutan, Nepal, and the Maldives, the remaining countries of present-day South Asia, were unaffected by the partition. The first two, Nepal and Bhutan, having signed treaties with the British designating them as independent states, were never a part of the British Indian Empire, and therefore their borders were unaffected by the partition of India. The Maldives, which had become a protectorate of the British crown in 1887 and gained its independence in 1965, was also unaffected by the partition.