Consider the following statements regarding the 80-pillared hall discovered at Kumrahar (Pataliputra): 1. Spooner's excavations at Kumrahar revealed a massive hall with 80 polished sandstone pillars arranged in 8 rows of 10 pillars each. 2. The pillars were made of Chunar sandstone and did not have any capitals. 3. The floor and roof of this hall were made of stone, representing the earliest use of stone vaulting in India. 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?