Step 1: Assigning Historical Dates/Periods to Each Event:
To arrange these ancient political developments chronologically, we must establish their respective timelines:
• I. Harshavardha in Kanuj: Harshavardha ruled the Vardha dysty from his capital at Kanuj during the early $7^{\text{th}}$ century CE ($c. 606$ -- $647 \text{ CE}$).
• II. Chandragupta Maurya in Pataliputra: Chandragupta Maurya founded the Mauryan Empire at Pataliputra in the late $4^{\text{th}}$ century BCE ($c. 321 \text{ BCE}$).
• III. Satavahas in Deccan: The Satavaha dysty ruled over parts of the Deccan and western India from approximately the late $2^{\text{nd}}$ century BCE to the early $2^{\text{nd}}$ century CE.
• IV. Chalukyas in Kartaka: The Early Chalukyas of Badami established their domint kingdom in the Deccan/Kartaka during the mid-$6^{\text{th}}$ century CE ($c. 543 \text{ CE}$ onwards).
Step 2: Chronological Arrangement:
Arranging them from the earliest to the most recent period:
$\text{II (c. 321 BCE)} \rightarrow \text{III (c. 2nd century BCE to 2nd century CE)} \rightarrow \text{IV (c. 6th century CE)} \rightarrow \text{I (c. 7th century CE)}$
The correct order is II, III, IV, I.
Step 3: Conclusion:
This sequence perfectly matches option (B).