The correct option is (b) leprosy.
Explanation:
To apply Koch's postulates, we have to culture the suspected causal organism in vitro. Mycobacterium leprae cannot be cultured in vitro. Hence, Koch's postulates are not applicable to leprosy because its incubation period is 2-5 years.
Cholera is caused by Vibrio cholerae.
TB is caused by Mycobacterium tuberculosis.
Diphtheria ls caused by Mycobacterium diphtheriae.