The given question asks for the full form of IRDAI. Let's evaluate each option:

International Relations Development Authority of India

This option is incorrect. 'International Relations Development Authority of India' does not relate to financial or insurance sectors, which IRDAI is associated with.

Irrigation and Rural Development Authority of India

This option is also incorrect. While it mentions 'development', it relates to agriculture and rural sectors, not to insurance.

Insurance Regulation and Developmental Authority of India

This option is incorrect due to two errors: firstly, 'Regulation' should be 'Regulatory', and secondly, 'Developmental' is not the correct form used in the official name.

Insurance Regulatory and Development Authority of India

This option is correct. IRDAI stands for 'Insurance Regulatory and Development Authority of India'. This is the statutory body responsible for regulating and promoting the insurance and re-insurance industries in India.

Therefore, the right answer is Insurance Regulatory and Development Authority of India. This entity is crucial for overseeing the insurance policies and ensuring the financial stability and legal compliance of the industry in India. It's a key regulatory body under the government of India.