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a). I’m going X home.
Ans: no article needed
b). the school that I went to has closed down now.
Ans: the
c). He’s in X hospital
Ans: no article needed
d). When I began life at X university, I was quite naive.
Ans: no article needed
e). Let’s have X dinner tomorrow.
Ans: no article needed
f). I’m going to Taiwan for X Chinese New Year.
Ans: no article needed