Being a paediatrician, I would dare to answer only the first question.
I would like to know bit more in the history ie, parents age of onset of puberty. Even without considering the history,
answers c, d and e can be easily discarded.
The commonest reason for the problem is
Constitutional Delay in Growth and Puberty (CDGP).
Approximately 15% of patients of short stature referred for endocrinologic evaluation have CDGP. Individuals with CDGP superimposed upon familial short stature represent another 23%. The frequency of CDGP may be underestimated because individuals with milder delays and those who are not psychologically stressed may not be seen by subspecialists.
Most of them do well, gain puberty and attain final predicted height, if we wait and watch for a year or two.
Testosterone
may (not should) be given in some cases to kick start the pubertal process if there is excessive delay and if the child is experiencing psychological distress.
My answer will be
A.
Please look at this very useful link:
Constitutional Delay in Growth and Puberty