Answer: a) leader-member exchange
Explanation:
Leader-member exchange(LMX) theory is defined as the theory that states about relationship between the managers and the workers should be respectful, interactive ,emotional and faithful so that the workplace environment can be efficient and productive.
According to the situation described in question, Monisha is considered as the best worker by Franz because he knows that she can complete the task successfully as he trusts her .Franz believe on Monisha is due their interaction and faith on each other. Thus, Monisha is able to achieve the goal .
Other options are incorrect because life cycle theory states about life cycle of something. Alternative or replacement for leadership is not being done neither goal through dedicated direction is achieved. Vroom-Yetton-Jago is related with leadership based on situation.
Thus the correct option is option(a)