But here in the first blank it is talking about that how the discussion over cheating is about to go prevalent, hence shouldnt the answer be 'Expedite' ?

The discussion can be impeded by the fact that both sides diverge in the meaning they give to cheating. That is the meaning of the first sentence.

Moreover, the all three blanks must be in accordance to fit in the sentence.

If we thing that the discussion must be speeded up and then the second blank is about the different meaning they give to cheating as significance, I do not see how they can give meaning to the sentence as a whole!!!

The correct words for the blanks are (i) hampered, (ii) disparate, and (iii) impediment to.

Breakdown of the Blanks
- Blank (i): C. hampered

The sentence states that a campus-wide discussion on academic integrity is negatively affected by the fact that faculty and students have different definitions of cheating. Hampered means to hinder or impede the movement or progress of. This fits the context of the discussion being hindered by differing views.
- Blank (ii): D. disparate

The sentence explains that the reason for the difficulty is that faculty and students define cheating in " $\qquad$ ways." Disparate means different in kind; not able to be compared. This word perfectly describes the different and conflicting definitions of cheating.
- Blank (iii): H. impediment to

The final blank describes the effect of the differences in how cheating is defined and the severity assigned to it. It says these differences serve as a "major $\qquad$ " for creating common standards. Impediment to means a barrier or a hindrance to something. The differences act as a major barrier to creating consistent standards.

The Complete Sentence
"Campus-wide discussion on academic integrity can be hampered by the fact that faculty and students tend to define cheating in disparate ways. Even when they concur on what cheating means, faculty and students often assign different levels of severity to specific violations. These differences can serve as a major impediment to the creation of a commonly accepted set of standards of integrity that are consistently applied to all academic work within the campus community."