Given below are two statements, one labeled as Assertion (A) and the other labeled as Reason (R). **Assertion (A):** A mirage is observed in hot deserts when light rays from the sky bend upwards near the ground. **Reason (R):** The refractive index of air increases with height above the hot ground, causing light rays to bend away from the normal as they travel downwards. Select the correct answer using the codes given below:
Options:
- A: Both A and R are true and R is the correct explanation of A.
- B: Both A and R are true but R is not the correct explanation of A.
- C: A is true but R is false.
- D: A is false but R is true.
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?