The Hindu Marriage Act, 1955 does not allow marriage between first cousins. The marriage would be void, unless the custom of the community permits it.
According to the conditions laid down in the Act for a marriage to be valid, one of the conditions is that the parties should not be within the degrees of prohibited relationships, unless the customs or usage, permits such a marriage.
Two persons are said to be within the degrees of prohibited relationships:
1. if one is a lineal ascendant of the other.
2. If one was the wife or husband of a lineal ascendant or descendant of the other.
3. if one was the wife of the brother or of the father’s or mother’s brother or the grandfather’s or grandmother’s brother of the other.
If the two are brother and sister; uncle and niece; Aunt and Nephew or children of brother and sister of two brothers or two sisters.
In the present case, since marriage between first cousins is considered illegal, so would be the relationship if they lived together.
Though there is no law that prohibits cousins from coming together in a live in relationship at the same time Courts have previously held that live in relationships between cousins would be considered illegal.
In 2010, The Bombay High Court has refused to allow a plea of a boy for a live in relationship with his cousin since their marriage could not materialise in view of prohbited degrees of relationship.
Reference: Hindu Marriage Act, 1955