In which year did British India witnessed the famous 'Cotton Boom'?

1861

The correct answer is Option (2) → 1861

Timeline of important events in 18th and 19th century India:

1765: English East India Company acquires Diwani of Bengal
1773: Regulating Act passed by the British Parliament to regulate the activities of the East India Company
1793: Permanent Settlement in Bengal
1800s: Santhals begin to come to the Rajmahal hills and settle there
1818: First revenue settlement in the Bombay Deccan
1820s: Agricultural prices begin to fall
1840s-50s: A slow process of agrarian expansion in the Bombay Deccan
1855-56: Santhal rebellion
1861: Cotton boom begins
1875: Ryots in Deccan villages rebel

When the American Civil War started in 1861 cotton from the American South stopped coming into the international market. This led to an upsurge in demand for Indian cotton, grown primarily in the Deccan. Once again Indian merchants and middlemen found an opportunity for earning huge profits. In 1869 the Suez Canal was opened and this further strengthened Bombay's links with the world economy.