The Doctrine of Lapse, under which a state was annexed if its ruler died without a natural heir, was applied most widely by Governor-General:

The Doctrine of Lapse was applied most widely by Lord Dalhousie, the Governor-General of India from 1848 to 1856.

About the Doctrine of Lapse:

• According to this policy, if the ruler of a dependent state died without a natural (biological) male heir, the state would "lapse", that is, pass to the Company.
• The ruler's adopted son would not be recognised as the heir to the kingdom, though he could inherit the ruler's personal property.
• This went against the Indian custom of adoption, under which an adopted son had full rights.
• The idea had been used occasionally before, but Dalhousie applied it systematically.

NCERT on the Doctrine of Lapse:

• NCERT notes that under Dalhousie, the Company devised a policy that came to be known as the Doctrine of Lapse.
• The doctrine declared that if an Indian ruler died without a male heir, his kingdom would "lapse", that is, become part of Company territory.
• One kingdom after another was annexed simply by applying this doctrine: Satara (1848), Sambalpur (1850), Udaipur (1852), Nagpur (1853) and Jhansi.

States annexed under the doctrine:

• Satara: the first state to be annexed (1848).
• Jaitpur and Sambalpur.
• Baghat.
• Udaipur (in Chhattisgarh, not Rajasthan).
• Nagpur, the large kingdom of the Bhonsles.
• Jhansi.

Other policies of Dalhousie:

• He annexed Punjab and Lower Burma after wars.
• He introduced the railways (Bombay to Thane, 1853), the telegraph and the modern postal system.
• He set up a separate Public Works Department.

Results:

• The Doctrine of Lapse caused great resentment among the Indian rulers, and was one of the causes of the Revolt of 1857.
• It was withdrawn after the Revolt.

Why not the other options?

• ✗Wellesley, Cornwallis and Hastings were earlier Governors-General with other policies.