Which of the following is a useful pivot word?
a. car
b. kitty
c. where
d. cookie

taking into account that a theme is the central topic a text treats and can be developed through a story, play, poem etc. the following are themes that can be further developed:  

my best friend jeffrey has many unusual interests. (the story could be about each of the unususal interests)

once a man gives his soul over to evil, he can never go back. (this could be a saying or a proverb)

the three sheepdogs lay around the yard all day. (it could be developed detailing how each of these sheepdogs lay around)

a priest's collar has an unusual effect upon people. (it could be developed detailing the different effect upon people)

innocence is a powerful force in a world full of corruption. (it could be developed detailing how is a world full of corruption)

king lear is a play shakespeare wrote later. (it is just a sentence and doesnt give any idea or topic to be discussed in details.

evil often wears the disguise of innocence. (this could be a saying or a proverb)

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).

it is a hope this 's

we need to see the examples!