The organization that links all the ATMs in India is the National Payments Corporation of India (NPCI), Option 3.

The NPCI is a not-for-profit organization founded in 2008, with the objective of creating a robust payment infrastructure in India. One of its flagship products is the National Financial Switch (NFS), which links all the ATMs in India.

NFS is a network of shared ATMs that allows customers of one bank to use the ATM of another bank. This interoperability allows customers to withdraw cash and perform other banking transactions seamlessly across different banks, without having to visit a branch.

The NPCI has also launched other digital payment products, such as Unified Payments Interface (UPI), Bharat Bill Payment System (BBPS), and RuPay, which have revolutionized the way people make payments in India.

In contrast, the other options listed in the question do not link all the ATMs in India. Here`s why:

1. Indian Banks’ Association (IBA): The IBA is a voluntary association of banks in India. While it works towards promoting and coordinating the interests of its member banks, it does not have the mandate or the infrastructure to link all the ATMs in India.

2. National Securities Depository Limited (NSDL): The NSDL is a depository that provides electronic securities depository services. It is not involved in linking ATMs or facilitating banking transactions.

4. Reserve Bank of India (RBI): The RBI is India`s central bank, responsible for regulating the banking and financial sector in the country. While it has the authority to issue guidelines and regulations on ATM operations, it does not directly link all the ATMs in India. That role is fulfilled by NPCI.

Therefore, the correct answer to the question is Option 3: National Payments Corporation of India (NPCI).