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Correct Option is demonstrate

Solution:The concerned sentence states that the faculty members are expected to demonstrate continuous academic "production," which includes research, teaching, and societal contributions. Thus, we can infer that ‘demonstrate’ is the most suitable filler. Hence, option (b) is the right answer choice.
(a) abnegate- renounce or reject (something desired or valuable).
(b) demonstrate- clearly show the existence or truth of (something) by giving proof or evidence.
(c) proliferate- increase rapidly in number; multiply.
(d) condemn- express complete disapproval of; censure.
(e) improvise- produce or make (something) from whatever is available.

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