it will be insulator because band is completely filled....to solve sach type of questions..we have to analyze that band is completely fiiled , partially filled or empty ...on the b...
here you need to Find Neff for a certain band .. and then determining whether the band is full or empty you need to conclude whether is it metal or insulator
and it's not always true that nearly free electron model will always lead to metals.. This is free electron model theory .. where free electron is just an approximation.. this type...
ans is metal because we are dealing with nearly free electron approximation means outer most electron is almost free and that situation is possible in metals.