Analyze the political conditions in Bihar and Bengal on the eve of Bakhtiyar Khalji's military incursions: 1. The decline of the Later Palas left Bihar fragmented into small, weak principalities ruled by local chieftains without a centralized defense. 2. Constant territorial conflicts between the Sena Dynasty of Bengal and the Gahadavala Dynasty of Kannauj over Bihar prevented a unified regional alliance against the Turks. 3. The Sena rulers maintained a highly centralized standing army with advanced cavalry units stationed permanently along the western borders of Bihar. Which of the statements given above are correct?

Options:

• A: 1 and 3 only
• B: 2 and 3 only
• C: 1 and 2 only
• D: 1, 2 and 3

Related Practice Questions:

• Let $S_1$ and $S_2$ be two disjoint, non-empty convex sets in $\mathbb{R}^n$. Under which of the following conditions is there guaranteed to exist a hyperplane that strictly separates $S_1$ and $S_2$?
• Let the primal linear programming problem be: Maximize $Z = c^T x$ subject to $Ax \le b, x \ge 0$. If this primal problem has an unbounded optimal objective value, then which of the following statements is always true regarding its dual problem?
• Let $S = \{(x, y) \in \mathbb{R}^2 \mid x^2 + y^2 \le 9\}$ be a convex set in $\mathbb{R}^2$. The set of all extreme points of $S$ is given by:
• In a linear programming problem with $3$ independent equality constraints and $5$ variables (including slack/surplus variables), what is the maximum possible number of basic solutions?