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After passing through polaroid A, the intensity becomes $I_1 = \frac{I_0}{2}$.

According to Malus's Law, after passing through polaroid B:

$I_2 = I_1 \cos^2 \theta = \frac{I_0}{2} \cos^2(45^\circ) = \frac{I_0}{2} \times \left( \frac{1}{\sqrt{2}} \right)^2 = \frac{I_0}{4}$.

We need $0 < st < 1$, meaning $st$ is a small positive number. This requires $s$ and $t$ to have the same sign.

• Option A: $s < -1, t > 0$ → $st < 0$. Not possible.
• Option B: $s < -1, t < -1$ → both negative, so $st > 0$. For example $s = -2, t = -0.3$: $st = 0.6$, which satisfies $0 < st < 1$. ✓
• Option C: $s > -1, t < -1$ → could give $st$ negative or positive depending on sign of $s$. If $s = 0.5, t = -2$: $st = -1 < 0$. Not valid for all cases.
• Option D: $s > 1, t < -1$ → $st < -1 < 0$. Not possible.

Option B is the one that can satisfy the condition.

Management of unconscious hypoglycemic patient:

• NEVER give anything orally to an unconscious patient — risk of aspiration
• IV Dextrose 50% (D50W) — 25–50 mL IV push is the immediate treatment for unconscious hypoglycemia
• If IV access unavailable: Glucagon 1 mg IM/SC (stimulates hepatic glycogenolysis)

For conscious patients: oral glucose (15g fast-acting carbohydrates — 4 glucose tablets, 125 mL juice) → Rule of 15:

\\text{Give 15g carbohydrates} \\rightarrow \\text{Wait 15 min} \\rightarrow \\text{Recheck glucose} \\rightarrow \\text{Repeat if still} < 70 \\text{ mg/dL}

Critical distinction: In this question, the patient is unconscious — oral route is contraindicated. D50W IV is the answer.