Option 1 is correct because after the independence of India, the British Government granted freedom to the princely states to decide whether they wanted to join either India or Pakistan or to remain independent.

Option 2 is also correct. The decision was indeed left not to the people of the princely states but to the rulers. This led to significant issues in some states, such as Jammu & Kashmir, where the Maharaja decided to join India against the wishes of the majority Muslim population.

Option 3 is correct. Initially, the ruler of Travancore announced the independence of his state with the intention of forming a new country. However, later he decided to join the Indian Union due to internal and external pressures.

Option 4 is incorrect thus making it the right answer to the question. The State of Travancore joined Indian Union not through a plebiscite but through signing the ‘Instrument of Accession’ by the ruler. A plebiscite implies a direct vote by all the people of the state, which did not happen in case of Travancore.