My take:

A - Correct: "paper of all kinds IS" used the right verb, second clause is concise.
B - Same right verb use but second clause is unnecessarily wordy.
C - "paper of all kinds ARE" is incorrect
D - "All kinds of paper ARE" is correct but "and so" is unidiomatic
E - "All kinds of paper IS" is incorrect

A should be the answer !
Because and "so that" in the same sentence is redundant.
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Because paper of all kinds is the biggest single component of municipal trash, many municipalities have tried recycling to reduce the cost of trash disposal.

(A) Because paper of all kinds is the biggest single component of municipal trash, many municipalities have tried recycling to reduce the cost of trash disposal.
Didn't see any problem with it, hold it still.

(B) Because paper of all kinds is the biggest single component in municipal trash, many municipalities tried to recycle so that the cost of trash disposal is reduced.
the word "in" as a preposition here is NOT idiomatic.
and I think the ''is'' in "cost of trash disposal is reduced" should be ''will be''
and ''so that'' sounds redudant here.

(C) Because paper of all kinds are the biggest single components of municipal trash, many municipalities have tried to recycle to reduce the cost of trash disposal.
Simple gramatical error.

(D) All kinds of paper are the biggest single components of municipal trash, and so many municipalities have tried recycling to reduce the cost of trash disposal.
The subject should be "paper", not "all kinds"
''and so'' is redundant and incorrect here.

(E) All kinds of paper is the biggest single component of municipal trash, so many municipalities have tried to recycle so that the cost of trash disposal could be reduced.
Same reason as the last one, plus the incosistent usage of "kinds" and "is" and ''have'' and ''coule be''

My choice is A

D and E are eliminated because the subject is "paper" and NOT "the kind".

C "paper of all kinds are" incorrect because paper -singular and we need IS not ARE.

B i eliminated B because only in one of five answer choices we see "component in", so i diceded that this is incorrect one. Because if this is correct it would be very strange.

So i stayed with A

+1 A
Paper + prepositional phrase( of .......) Singular thus takes singular verb IS
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