Valid IP Address: 192.168.1.1

Explanation:
An IP address is a unique numerical label assigned to each device connected to a computer network that uses the Internet Protocol for communication. It is made up of four sets of numbers separated by periods, ranging from 0 to 255.

To determine whether an IP address is valid or not, we need to consider the following rules:

1. Each set of numbers in the IP address must be between 0 and 255.
2. Each set of numbers should not contain leading zeros (except for the number zero itself).
3. There should be exactly four sets of numbers separated by periods.

Let's analyze each option:

a) 192.168.111.1111
This IP address has an extra digit in the last set of numbers. The maximum value for each set is 255, so 1111 is not a valid number. Therefore, option a) is not a valid IP address.

b) 192.168.1.1
This IP address meets all the rules. Each set of numbers is between 0 and 255, there are no leading zeros, and there are four sets of numbers separated by periods. Therefore, option b) is a valid IP address.

c) 192.168.900.1
This IP address has a number (900) in the third set that is greater than 255. According to the rules, each set must be between 0 and 255. Therefore, option c) is not a valid IP address.

d) 192.900.168.1
This IP address has a number (900) in the second set that is greater than 255. According to the rules, each set must be between 0 and 255. Therefore, option d) is not a valid IP address.

e) None of these
This option indicates that none of the given options is a valid IP address, except for option b) which is a valid IP address.

In conclusion, the valid IP address among the given options is option b) 192.168.1.1.