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What is Normal size but non functioning uterus is usually associated with: and explain in detail?
Lets have a look at each option:
Option a: Stenosis of external os would result in hematometra, i.e. uterus would be large and non functioning (hence ruled out).
Option c: Partial agenesis of vagina 
In parital agenesis of vagina a segment of vagina may be atretic in the upper-third. It is often associated with hypoplasia or even absence of cervix. Uterus may be normal and functioning or malformed.
Option d: Complete absence of vagina is almost always associated with absence of uterus.
Hence by exclusion our answer is b i.e. uterine synechiae (Asherman syndrome)
In Uterine syechiae–the uterus does not function normally due to presence of adhesions size of uterus is normal.