Who was the first Governor General of India appointed by Britishers?

William Bentick

The correct answer is Option 2- William Bentick

The title "Governor-General of India" wasn't always used historically. For clarity:

First Governor-General of Bengal: If you consider the position of Governor-General in the context of just Bengal (a British East India Company presidency), then the first would be Warren Hastings in 1773.
First Governor-General of British India: However, the title "Governor-General of India" came into effect with the Government of India Act 1833. In this context, the first Governor-General of British India was Lord William Bentinck in 1833.