With reference to the scientific and mathematical contributions of Aryabhata, consider the following statements: 1. Aryabhata formulated the rule for finding the area of a plane triangle as half the product of the base and the height. 2. In Aryabhatiya, he explicitly stated that the Earth is spherical and rotates on its own axis, causing day and night. 3. He calculated the value of Pi (π) to be 3.1416, which he described as an approximate (asanna) value. Which of the statements given above is/are correct?
Options:
- A: 1, 2 and 3
- B: 1 and 2 only
- C: 2 and 3 only
- D: 1 and 3 only
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?