India's seizure of control over Kashmir in 1947 was primarily a result of the political situation following the partition of British India. The princely states, including Jammu and Kashmir, had the option to join either India or Pakistan.
When the ruler of Jammu and Kashmir, Maharaja Hari Singh, initially decided to remain independent, tribal invasions from Pakistan in October 1947 forced him to reconsider. Facing a crisis, the Maharaja sought military assistance from India, which led to a conditional agreement. He signed the Instrument of Accession on October 26, 1947, agreeing to join India, which was later accepted by the Indian government.
Thus, while the options concerning the region's membership were influenced by historical routes, demographics, and agreements, the most relevant reason for India's control over Kashmir in 1947 was the Maharaja's decision to accede to India in response to external threats.
None of the answer choices presented are fully accurate or encompass the complexity of the situation, but the closest would be "Pakistan had agreed to India’s takeover" in the sense that Pakistan's aggression helped catalyze India's control of the region through the accession agreement.