Explanation

Start with the last blank because it is the easiest. The clue tells you that the plaintiff’s case disintegrated. Therefore, the claims must have been shown to be false. Facetious, though somewhat negative, does not mean false but does not go far enough. Unerring goes in the
opposite direction. Specious is the best match. The first blank is the easiest one to attempt next. The case fell apart when something happened to the witnesses’ credentials, so a goodphrase for the first blank—which described the role of the witnesses in the plaintiff’s case—is “based on.” Dependent on is the only match.

If the plaintiff’s claims were based on the witnesses, and the case fell apart, logically the witnesses must have been discredited somehow.

A good word for the second blank—which describes what the court decided about the witnesses’ credentials—is denied. Vindicated goes in the opposite direction. Repudiated is the best match.

Hence options C, E and I are correct!
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Why not B,D,I?

I mean if the accusations from the plaintiff were totally isolated from the testimony of the two witnesses and if the vindicated their credentials, the plaintiff's case disintegrated and also the claims were shown to be false.

Doesn't this also make sense?

plaintiff - a person who brings a case against another in a court of law
subservient- subordinate
vindicated - to show to be right by providing justification or proof
repudiate - refuse
facetious - jocular
unerring - Consistently accurate
specious - plausible but false

we will start from 2nd line -

Therefore, when the court _____(ii)_____ the credentials of those witnesses, the plaintiff’s case disintegrated,

since the case was dismissed -
so easily we can guess - the credential was refused.
so blank 2 repudiated fits perfectly

case was disintegrated by the court after refusing the credentials of those witnesses.
when it will happen??
when the case is fully dependent on the witness, isnt it?
so blank 1 fits - dependent on

blank 3 is easy now-
and give us same connotation
witness credential was surely false
specious - fits perfectly

answer -
dependent on
repudiated
specious

hope this will help.
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