Option 1: Hyderabad - This state was forced to merge itself with the Union of India after 1947. Hyderabad was ruled by the Nizams, who initially wanted the state to become independent. However, due to a turbulent political situation and pressure from the Indian government, Hyderabad was eventually annexed by India in 1948 through a military intervention called Operation Polo. This resulted in the merger of Hyderabad into the Indian Union.

Option 2: Kashmir - Although Kashmir has faced political conflicts and military interventions, it was not forced to merge with the Union of India after 1947. Kashmir`s accession to India was based on a legal agreement, known as the Instrument of Accession, signed by the Maharaja of Kashmir, Hari Singh.

Option 3: Patiala - Patiala was a princely state in British India, but it was not forced to merge with the Union of India after 1947. It willingly acceded to India in 1948.

Option 4: Mysore - Mysore, which is now known as Karnataka, was also not forced to merge with the Union of India after 1947. It voluntarily acceded to India in 1947.

Therefore, the correct answer is option 1: Hyderabad.