Consider the following statements regarding the geopolitical context of the capital shift from Rajgir to Pataliputra: 1. The defeat of the Vajjis and Kasis by Ajatashatru shifted the geopolitical center of gravity of Magadha further north. 2. Pataliputra offered a central location to administer the newly annexed territories of Vaishali and Anga. 3. The threat of invasion from the Avanti kingdom under Pradyota made the open plains of Pataliputra safer than the hilly Rajgir. Which of the statements given above is/are correct?
Options:
- A: 1 and 3 only
- B: 1 and 2 only
- C: 2 and 3 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?