what was the relationship between these states and british?
Tense, the British used  different policies to rule them Policy of annexation and Policy of indirect rule
Political integration of India
The first was a policy of annexation, where the British sought to forcibly absorb the Indian princely states into the provinces which constituted their Empire in India. The second was a policy of indirect rule, where the British assumed suzerainty and paramountcy over princely states, but conceded to them sovereignty and varying degrees of internal self-government.
which state became part of india after independence Territories under British rule the suzerainty of the British Crown and princely states what was the reason that it was integrated? Because of India's independence were any states merged? Yes the princely states
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Political integration of India [SEP] Princely states in India
The early history of British expansion in India was characterised by the co-existence of two approaches towards the existing princely states. The first was a policy of annexation, where the British sought to forcibly absorb the Indian princely states into the provinces which constituted their Empire in India. The second was a policy of indirect rule, where the British assumed suzerainty and paramountcy over princely states, but conceded to them sovereignty and varying degrees of internal self-government. During the early part of the 19th century, the policy of the British tended towards annexation, but the Indian Rebellion of 1857 forced a change in this approach, by demonstrating both the difficulty of absorbing and subduing annexed states, and the usefulness of princely states as a source of support.