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Set of possible strings generated by Regular expression (11+111)* should contain {null, {11}, {111}, {11111},…}. Can this set contain the strings which are generated considering the part of the above RE partially, i.e., will {1111} (length 4), generated by considering either {11} partially or {111} partially. Can such string be a part of the language ?

Yes $1111$ should be in the language due to by making $*$ as $2$ and choosing $11$ both times.

@ thanks for answering, as per my understanding from your answer, we are accepting the string(s) by making combinations(multiples of minimum length) of them, i.e., (11)* can have {null, 11, 1111, 111111,...}. but still my doubt is can we have {1} also as a part of above Language set, as it is generated by taking (11)* as partially?

but still my doubt is can we have {1} also as a part of above Language set, as it is generated by taking (11)* as partially?

No you can not !

for simplicity, you can think like (11+111)* = (A+B)* , where A=11, B=111

then you can generate epsilon, A,B,AA,AB,BA,BB,......

for getting 1111 ---- you have AA, but for 1 -- you don't have anything