In the following questions, a few sentences are given. Identify the sentences that are grammatically and contextually incorrect.
(I) The students who have completed the assignments on time will receive extra credit from their instructor.
(II) Despite of the heavy traffic, we managed to reach the airport on time for our flight.
(III) She has been working on the project since six months, but there is still a lot left to do.

The correct answer is Both (II) and (III).

Let us analyze each sentence step-by-step to identify the grammatical errors:

Sentence (I): "The students who have completed the assignments on time will receive extra credit from their instructor."
This sentence is grammatically and contextually correct. The relative clause "who have completed..." properly modifies "students", and the verb usages and prepositions are all correct.

Sentence (II): "Despite of the heavy traffic, we managed to reach the airport on time for our flight."
This sentence is incorrect. The preposition "despite" is never followed by "of". We should either use "Despite the heavy traffic..." or "In spite of the heavy traffic...".

Sentence (III): "She has been working on the project since six months, but there is still a lot left to do."
This sentence is incorrect. "Since" is used to refer to a specific point in time (e.g., since Monday, since 2010), whereas "for" is used to specify a duration of time. Since "six months" is a duration, the correct preposition is "for six months".

Therefore, sentences (II) and (III) are grammatically incorrect.