Explanation:

- Option 1: A wife living in adultery cannot claim maintenance. The law denies maintenance to a wife who is unfaithful to her husband.

- Option 2: A wife living separately by mutual consent also cannot claim maintenance. When a couple agrees to live apart, it indicates a mutual decision, which negates the need for support.

- Option 3: Both (a) and (b). This choice combines the aspects of both adultery and mutual consent as reasons for ineligibility.

- Option 4: Either (a) or (b) means if either of the situations applies, the wife cannot claim maintenance.

Option 3: Both (a) and (b) is the correct answer.