Rohit
(E) provided with the best physical therapists, and trained carefully, Olympic runners will achieve
Here the only noun prior to the verb+ed participle is the coach; Can the participle in that case modify the coach? Is the coach the one provided with the best therapists and trained carefully?
Therefore, the existence of a rule alone does not decide a choice. The judicious application of the rule decides.
If you visit, the official example cited by Abhimana might help you in this regard.
Abhishek,
Of course, the first part is indeed a relative clause using a relative pronoun 'who' and a verb 'manages'. . After all, modifiers include relative clauses also.
Ex---A South American bird that forages for winged termites and other small insects while swinging upside down from the foliage of tall trees, the gaveteiro belongs to the ovenbird family, a group of New World tropical birds that includes more than 230 species and is represented in virtually every kind of habitat.
However, look at the context of the test case.
For the coach who manages to keep them uninjured, providing them with the best physical therapists, and training them carefully, Olympic runners are achieving upwards of 30 personal records each year.
(A) providing them with the best physical therapists, and training them carefully, Olympic runners are achieving
(B) providing them with the best physical therapists, and trained carefully, the Olympic runner achieves
(C) providing with the best physical therapists, and training them carefully, Olympic runners are achieving
(D) providing with the best physical therapists, and trained carefully, the Olympic runners achieves
(E) provided with the best physical therapists, and trained carefully, Olympic runners will achieve
If providing 'them' were to refer to the Olympic runners, it is not clear what the word 'them' refers to. Does it mean that the runners are providing themselves or training themselves? In that case, the coach becomes infructuous. In addition it is not within reason to say that the Olympians are producing personal records for their managers rather than for their countries and for themselves.