This sentence might be difficult because of the temptation to ignore the word “diet.”  In actuality, this word is the most specific and matching for our purposes.  The word is used to name the legislative assemblies of some countries and hence is a better option than “group” or “congregation,” which do not match as well.   For example, in the city of Worms in 1521, an assembly gathered to address the questions related to Martin Luther.   This formal gathering is famously called the “Diet of Worms.”  As you can see, it has nothing to do with strange eating habits.  It merely means that an assembly within the Holy Roman Empire happened to convene at a city named “Worms.”

Although we often think of “orthodoxy” as being associated with religious beliefs, it is also applicable to any theory or doctrine, meaning that it is authoritative and generally held.  This word is the best option, given the adjective “unquestioned,” which does imply that the needed word have sense of implying a certain authority.  The word comes from the combination of “ortho,” meaning “straight” or “correct” and “doxos” meaning “opinion” (or “praise.”)  An “orthodontist” works to make teeth (“-dontist”) be straight (“ortho-”).  A “paradox” is something that seems to be different from the accepted opinion (“doxos”).

The key thing to note here is that these businesses are choosing to have their computers placed in a place that hosts them together with the computers for other businesses.  These computers share the same location (or are located “next to” each other in such a center).  “Collocation” indicates such “locating together,” as can be seen by the parts of the word.  “Col-” comes from the prefix “Co-” or “Con-”, meaning “together with” and is found in words like “colloquy” and “cohabitate.”  The second half, “location,” is obvious in its meaning.

Although any of these options apply to certain kinds of mental failure, the best option is the general one—“senility.”  This likewise can apply to the general loss of strength in way that the others cannot.  The word “senility” first indicates the general signs of aging and weakening from that.  It does especially apply to loss of mental ability, though not solely that.  The word is derived from the Latin word for old man, “senex.”  It is related not only to the English “senile” but also “senior,” as well as “senator.”  The last title was chosen because such lawmakers are intended to be the “wise old men” of the country.

Since the foreign government wishes the United States to send the man to their country for trial, such an act would best be called an “extradition.”   To “extradite” someone is to send them to be tried in a country in which they committed a crime.  The word is a compound of the prefix “ex-,” meaning “out of” (found in many English words like “exit,” “exfoliate,” and “expropriate”) and the latter portion “-tradition.”  This latter half comes from the Latin for “to hand over” (itself a compound), as can be seen in the very form found here “tradition,” a word literally meaning “something handed over (e.g. from generation to generation).” 

The sense of this sentence is that drinking too little water is connected with the occurrence of migraine headaches, although we cannot say if there is a direct causality.  When two things at least occur at the same time (even if you cannot claim causality) they are said to be “concomitant,” a word meaning “occurring at the same time as something else.”  Think of it as meaning “sharing the same company (-comitant) with (con-) something else.”

The key trait emphasized in this sentence is Aaron’s tendency to continue to speak.  Therefore, he is not known for brevity.  “Silence” is too strong of an option, and the other wrong answers bring to bear some other character trait.  The word “breviloquence” is a rare English word, but its parts can be discerned.  The “brevi-” portion is clearly related to the word “brevity” or “brief.”  The second half “-loquence” comes from the Latin for “to speak” and is found in other words like “eloquent,” “elocution,” and “colloquy.”  Therefore, “breviloquence” means “being brief in speech.”

Since the sentence does not indicate any specific means by which the water was being supplied, the best option will be the one that is most general, only implying the general function of “carrying water.”  The word “aquifer” is derived from Latin roots literally meaning “water carrying.”  The “aqui-” portion clearly indicates water as is evident in related words like “aquarium” and “aquatic.”  The “-fers” portion comes from the base for “to carry,” found in “differ” (lit. to carry away from something else) and “transfer” (lit. to carry across).

The specific sense that we are looking for in our word is that of forgiveness and mercy.  While Albert’s act is perhaps pious and generous, it most certainly is “clement,” a word meaning “lenient or merciful.”  When we say that there is “inclement weather,” we generally mean that it is particularly nasty, as though it were unforgiving.

Clearly, the mother in question is neither stealing nor succeeding to the throne.  However, insofar as she is ruling, she is doing so as a replacement for the king.  A person filling such a role is called the “regent.”  Such regency is undertaken in any case where the normal ruler is not fit to assume responsibilities (e.g. because of age, illness, or perhaps being off at war and out of communication).  The word is related to the Latin “regere,” meaning “to rule.”  Related words in English include “regal,” “reign,” and “interregnum.”