Step 1: Understanding Jahangir's ascent to power.
Jahangir became the ruler of the Mughal Empire in 1605 after the death of his father, Emperor Akbar. He ruled the empire for 22 years until his death in 1627.
Step 2: Analyzing the options.
(A) 1605: Correct. Jahangir ascended the throne in 1605 following Akbar's death.
(B) 1610: This is incorrect, as Jahangir became the ruler in 1605, not 1610.
(C) 1620: This is incorrect, as Jahangir had already become the ruler by 1620.
(D) 1627: This is incorrect, as 1627 was the year of Jahangir's death, not his ascension.
Step 3: Conclusion.
The correct answer is (A) 1605, as Jahangir became the ruler of the Mughal Empire in that year.