The state of Jhansi was annexed by Lord Dalhousie under the Doctrine of Lapse in:

The state of Jhansi, in Bundelkhand, was annexed by the English East India Company under the Doctrine of Lapse in March 1854.

Background:

• Jhansi was ruled by a Maratha family of the Newalkar clan, which had come under British protection in the early 19th century.
• Raja Gangadhar Rao, the ruler of Jhansi, had no surviving son.
• A day before his death in November 1853, he adopted a boy, Anand Rao, who was renamed Damodar Rao, in the presence of a British officer.
• He wrote to the British, asking that the adopted son be recognised as heir, and that his widow, Rani Lakshmibai, be allowed to rule as regent during the boy's minority.

The annexation:

• The Governor-General refused to recognise the adoption for the purpose of succession to the throne.
• Jhansi was declared to have "lapsed" to the Company and was annexed in March 1854.
• The Rani was given a pension of 5,000 rupees a month and was asked to leave the fort; she remained in the palace in the town.
• She appealed against the annexation, with the help of a British lawyer, John Lang, but her appeal was rejected.
• The Company also deducted the late Raja's debts from her pension, and allowed cow slaughter in Jhansi, which hurt local feelings.

Results:

• The annexation caused deep resentment, and the Rani became one of the most famous leaders of the Revolt of 1857.
• Her famous words, "Main apni Jhansi nahi dungi" ("I will not give up my Jhansi"), became a symbol of resistance.

Other states annexed under the Doctrine of Lapse:

• Satara (1848), Sambalpur (1850), Udaipur (1852) and Nagpur (1853), according to NCERT.
• The Doctrine of Lapse was withdrawn after the Revolt of 1857.

Why not the other options?

• ✗1848 was the year of the annexation of Satara.
• ✗1853 was the year of the Raja's death.
• ✗1856 was not the year of Jhansi's annexation.