$($a$)$ The ciphertext $\backslash ($ M E R G D B Z I K C A P $\backslash )$ is obtained by using Vigenere cipher with the key $\backslash ($ K N T R $\backslash )($the key length is $4).$ Find the plaintext.

$($b$)$ A password consists of $20$ hexadecimal characters. Each of the first ten hexadecimal characters in the password is independently and randomly generated. The next ten hexadecimal characters in the password are identical to the first ten hexadecimal characters. What is the entropy of the password?