**Core Concept**
In cases of head injury with hypotension and tachycardia, the choice of anesthetic agent for induction is critical to ensure adequate cerebral perfusion. The primary concern is to avoid further decreases in blood pressure, which could exacerbate cerebral ischemia.

**Why the Correct Answer is Right**
Lidocaine is a vasodilator and can cause a further decrease in blood pressure, exacerbating hypotension and reducing cerebral perfusion. However, in this scenario, the primary concern is to avoid hypotension, not to induce it. **Etomidate** is the preferred choice for induction in this scenario because it is a vasopressor, which helps to maintain or increase blood pressure, thereby ensuring adequate cerebral perfusion. Additionally, etomidate has minimal effects on respiration and cardiovascular stability, making it an ideal choice for patients with head injuries.

**Why Each Wrong Option is Incorrect**
**Option A:** **Lidocaine** would worsen the patient's hypotension and potentially reduce cerebral perfusion, which is undesirable in a patient with a head injury.
**Option C:** **Ketamine** can increase heart rate and blood pressure, but it also has the potential to cause cerebral vasodilation, which may worsen intracranial pressure in patients with head injuries.
**Option D:** **Propofol** can cause significant hypotension, which may exacerbate cerebral ischemia in patients with head injuries.

**Clinical Pearl / High-Yield Fact**
Etomidate is the preferred choice for induction in patients with head injuries due to its ability to maintain or increase blood pressure, thereby ensuring adequate cerebral perfusion.

**Correct Answer:** C. Ketamine