The cricket council that was [A] / were [B] elected last March is [A] / are [B] at sixes and sevens over new rules.

The critics censored [A] / censured [B] the new movie because of its social inaccessibility.

Amit’s explanation for missing the meeting was credulous [A] / credible [B].

She coughed discreetly [A] / discretely [B] to announce her presence.

Cricket Council is a collective noun so it takes a singular verb. The reference is made to a group as a whole and not to an individual.
So correct option for 1st sentence is AA.
Censure implies harsh criticism.Censor means to put a ban on something objectionable.So Censure should be the correct answer here.
Credible means capable of being believed.Credulous means tending to believe without evidence.So credible should be used for 3rd sentence.
Discretely means distinct whereas discreetly means to carefully avoid social embarrassment or distress; tactful. So use of ' discreetly' is correct here.
Hence option D.