The correct option is (a).
Explanation
Following the decline of the Mughal Empire in the 18th century, the Sikhs organized themselves into a political and military confederacy. This period saw the rise of the Dal Khalsa and the formation of Misls (sovereign bands) before the eventual consolidation of the Sikh Empire.
Statement-wise Analysis:
- Statement 1 is Correct: By the late eighteenth century, the Sikh territories had expanded significantly. The loose confederation of Sikh chiefs (Misls) controlled the vast region extending from the Indus river in the west to the Jamuna (Yamuna) river in the east.
- Statement 2 is Incorrect: Throughout the majority of the eighteenth century, the Sikhs were not united under a single ruler. Instead, they were organized into a number of bands called jathas, and later misls. These groups often acted independently or in coordination as the Dal Khalsa, but there was no single monarch until the very end of the century.
- Statement 3 is Incorrect: Banda Bahadur led the Sikh uprising against the Mughals in the early eighteenth century (roughly 1708–1715) and established a distinct administration, but he did not unite the territories from the Indus to the Jamuna into a single stable kingdom. The unification of these diverse Misls into a consolidated Sikh Kingdom was achieved by Maharaja Ranjit Singh in 1799 (at the very end of the 18th century).
Key Takeaway:
In the late 18th century, Sikh polity was characterized by the Misl system (confederacies) covering the area between the Indus and Jamuna; unification into a single kingdom occurred later under Ranjit Singh.