Final answer:
a) honeypot is the type of server used to trap a hacker; it's a security mechanism designed to attract cyber attacks so they can be monitored and analyzed.
Step-by-step explanation:
The type of server you would install that is designed to trap a hacker is called a honeypot. A honeypot is a security mechanism that is set up to detect, deflect, or in some manner counteract attempts at unauthorized use of information systems. Generally, it consists of a computer, data, or a network site that appears to be part of a network, but is actually isolated, monitored, and used to lure in and track hackers. The other options mentioned like NAT (Network Address Translation), IPS (Intrusion Prevention System) and IDS (Intrusion Detection System) serve different purposes. NAT is used to map multiple local private addresses to a public one before transferring the information, IPS is used to prevent known threats from executing in a system, and IDS is used to detect and alert system or network administrators of malicious activities.