The correct answer to the question is option 1, which states that the Jammu and Kashmir Rifles is an infantry regiment of the Indian Army.

Option 2, which mentions that it is a battalion of the Rashtriya Rifles, is incorrect. The Rashtriya Rifles is a counter-insurgency force that operates in Jammu and Kashmir, and the Jammu and Kashmir Rifles is not a part of it.

Option 3, which suggests that the Jammu and Kashmir Rifles is the name of the Armed Police of the State of Jammu and Kashmir, is also incorrect. The Jammu and Kashmir Armed Police and the Jammu and Kashmir Rifles are two separate entities, with different roles and responsibilities.

Option 4, which says that the Jammu and Kashmir Rifles is a paramilitary force under the Ministry of Home Affairs, is also incorrect. The Jammu and Kashmir Rifles is not a paramilitary force, but an infantry regiment of the Indian Army.

Therefore, the correct answer is option 1.