The correct answer is Option 2: 1 and 3 only.

Explanation:

Payment Banks are a new category of banks in India that were introduced by the Reserve Bank of India (RBI) to promote financial inclusion in the country. Payment Banks are allowed to accept deposits (up to Rs. 2 lakhs per customer), issue ATM/debit cards, provide internet banking, facilitate money transfers, and sell insurance and mutual fund products. However, Payment Banks are not allowed to lend money or issue credit cards.

Now let`s take a look at each statement given in the question:

1. Mobile telephone companies and supermarket chains that are owned and controlled by residents are eligible to be promoters of Payment Banks.

This statement is partially correct. The RBI guidelines on Payment Banks do allow for entities other than traditional banks to become promoters of Payment Banks. However, only companies incorporated in India and owned and controlled by residents are eligible to be promoters of Payment Banks. Also, there are certain other eligibility criteria that must be met, such as a minimum net worth of Rs. 100 crores and a sound track record of three years.

2. Payment Banks can issue both credit cards and debit cards.

This statement is incorrect. Payment Banks are not allowed to issue credit cards. They can only issue ATM/debit cards, which can be used to withdraw cash and make purchases.

3. Payment Banks cannot undertake lending activities.

This statement is correct. Payment Banks are not allowed to undertake any lending activities, including giving loans, overdrafts, or any other kind of credit facility. The primary objective of Payment Banks is to promote financial inclusion by providing basic banking services to the unbanked population in India, especially in rural areas. By not undertaking lending activities, Payment Banks can focus on their core mission of providing easy and convenient access to banking services to the underserved sections of the society.

In summary, the correct answer is Option 2: 1 and 3 only.