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TCS Other Question

for a set of 5 true or false questions,no student has written all the correct answers and no two students have given the same sequences of answers.what is the maximum number of students in the classes for this to be possible? if x is a remainder of
[(a^b)+(c^a)]/c
and x is also factors of [(ax^2)+bx+c]
then find relation between a,b,c and x..