Solution
Regarding the statements about the passage, Both Statement I and Statement II are correct.
Statement I says: "The author upholds the Baconian theory because, according to him, despite being a genius, Shakespeare could not write the plays and sonnets that have come down to us under his name."
Statement II says: "He holds that Bacon was more resourceful than Shakespeare because he had the liberal education."
Both statements accurately reflect the author's position in the passage.
The author clearly states: "I have always thought that the strongest argument in favour of the Baconian theory was, that no man, however indubitable his genius, could have written the plays and sonnets that have come down to us under Shakespeare's name who had not the liberal education of Bacon."
This sentence directly supports both statements.
It affirms the author's belief in the Baconian theory (that Shakespeare didn't write the works attributed to him) and specifically cites Bacon's "liberal education" as the crucial factor that made him capable of creating these works, something Shakespeare supposedly lacked.
Hence, the correct answer is Option 1: Both Statement I and Statement II are correct.