Hello mehaksal,
The problem with both A and B is that "of" after "on the basis/grounds" is introducing a very awckward phrase.
"of" can only introduce phrases, but phrases are not appropriate when we're trying to express an action or other complex thought. Using "of" with phrases that attempt to serve this purpose leads to awckward sentences.
(1) I went to the hospital because of my getting ill.
The reason I went to the hospital is an action (I got ill) so using a phrase to express it makes the sentence awckward. A better sentence would be:
(2) I went to the hospital because I got ill
Notice that we replace "of + phrase" with a clause (a clause has a working verb), which is a much more appropriate way to express an action or complex thought.
In this sentence the author wishes to explain why building large hospital would be wasteful. The explanation (duplicate facilities should be avoided) is not just a "thing" but an action; a clause would be better than a phrase. In A & B, "avoidance of duplicated facilities" is very awckward. Get rid of them.
Of the remaining answers, only E correctly links the two ideas through cause and effect. The right sentence must explain that the second idea (duplicate facilities should be avoided) is the justification (the reason) for the first idea (large new hospital would be wasteful). To link the two ideas, we need something like "because", "since", "given that" or other transitions that can introduce a justification or reasoning for the first idea. Eliminate C and D
The presence of "if only" at the start of E should not throw you off. "if only because" is an idiom used to emphasize that the idea about to be introduced is justification enough, even though there may be other justifications.
Eg: You should wear your seat belt, if only because it will help me sleep at night.
In this sentence, the justification "it will help me sleep" is not necessarily the only reason you should wear your seat belt, but it is reason enough.
The answer is E
-Patrick