Step 1: Understanding the Concept:
Chronological questions require an understanding of broad historical eras.
In this list, we have an event from the Early Medieval period, the Late Medieval period, and two from the Modern period.
Arranging them requires identifying the exact years these transformative events took place.
Step 2: Detailed Explanation:
Let us analyze each event in detail:
1. Arab conquest of Sindh (712 CE): This is the earliest event on the list.
Led by Muhammad bin Qasim, the Arab forces of the Umayyad Caliphate invaded the Sindh region (modern-day Pakistan).
They defeated Raja Dahir, marking the first significant Islamic expansion into the Indian subcontinent.
2. Third Battle of Panipat (1761): This occurred in the mid-18th century.
It was a conflict between the Maratha Empire and the invading Afghan army of Ahmad Shah Abdali.
The Marathas were defeated, which checked their expansion and allowed British power to grow more easily in the vacuum that followed.
3. Non-Cooperation Movement (1920): This was the first major mass movement led by Mahatma Gandhi against British rule.
It was launched in protest against the Jallianwala Bagh massacre and the Rowlatt Act, and was supported by the Khilafat Movement.
4. Quit India Movement (1942): This was the final major mass struggle before independence.
Launched in August 1942 during World War II, Gandhi gave the "Do or Die" call to force the British to leave India immediately.
Step 3: Final Answer:
The order is 712 CE $\rightarrow$ 1761 $\rightarrow$ 1920 $\rightarrow$ 1942.
This corresponds to the sequence 4 $\rightarrow$ 3 $\rightarrow$ 1 $\rightarrow$ 2.
Hence, the correct option is (A).