all question of automata theory

1. Design a DFA of the following: i. Which does not contain the string "aba". ii. Begins and ends with the same symbol over {a,b}. iii. Starts with ab. iv. Contains the string "bba". v. Contains at least 4 a's. vi. Odd number of a's and even number of b's. 2. Design a NFA of the following: i. Which contains all strings over {a,b} that end with "abba". ii. Number of occurrences of 0,1 and 2 is a multiple of 3 . iii. Contains even number of a's and exactly two b's. iv. Ends with 01,12 and 21 over the alphabet {0,1,2}. v. Contains 01011 . 3. Convert the following NFA to DFA: 4. Minimize the following DFA using Mayhill Nerode Theorem