My wife had to visit a hospital nearby. The security guard offered to move our car for us, but while driving it, he accidentally hit the wall, damaging the AC and radiator. The repair cost is around ₹20,000. Is the hospital responsible for this?

Yes, the hospital is likely liable for the damage to your car. As the security guard was acting within the scope of his employment, the hospital is vicariously liable for his negligence. You can seek compensation from the hospital for the repair costs.