In India, the first Bank of limited liability managed by Indians and founded in 1881 was:

Correct Option (B):

The Oudh Commercial Bank, established in 1881 in Faizabad, Uttar Pradesh, holds the distinction of being the first commercial bank in India with limited liability that was managed by Indians. It functioned as a joint-stock bank until its eventual collapse in 1958.

Incorrect Options:

• Hindustan Commercial Bank (A) was founded much later in 1948, making it incorrect for the specified year of 1881.
• Punjab National Bank (C) was established in 1895 in Lahore, which is subsequent to 1881. It is notable for being one of the earliest Indian-managed banks that remains operational.
• Punjab and Sind Bank (D) was founded in 1908, significantly later than the year mentioned in the question.