The Mughal emperor who was ruling at the time of Ahmed Shah Abdali`s invasion of India was Shah Alam II. Let`s go through the other options to understand why they are not the correct answers.
Option 1: Bahadur Shah I was not the Mughal emperor during Ahmed Shah Abdali`s invasion. He ruled from 1707 to 1712, much before the invasion took place.
Option 2: Bahadur Shah II, also known as Bahadur Shah Zafar, was the last Mughal emperor. However, he ruled during the 19th century and thus was not in power during Ahmed Shah Abdali`s invasion in the 18th century.
Option 3: Shah Alam I, also known as Alamgir II, was the Mughal emperor before Ahmed Shah Abdali`s invasion. He ruled from 1754 to 1759, but he was ousted from power by Ahmed Shah Abdali himself.
Therefore, the correct answer is option 4: Shah Alam II. He was the Mughal emperor during Ahmed Shah Abdali`s invasion of India, which took place in the 18th century.