Statement - I : A unitless quantity cannot have a dimensional formula
Statement - II :  A dimensionless quantity cannot have a unit.

If a quantity is unitless, it can not have dimensions, because dimensions imply units (in terms of M, L, T etc.).But the converse is not true since a quantity can be dimensionless and still have units (eg. Angular displacement). I is wrong.

A dimensionless quantity may have a unit but cannot be expressed in terms of seven fundamental SI quantities. For example, angle is a dimensionless quantity with unit radian but radian cannot be expressed in fundamental SI quantities. II is correct.