For a set of five true or false questions, no student hs written the all correct answer and no two students have given the same sequence of answers. What is the maximum number of students in the class for this to be possible?

Answer

31

Explanation

Clearly there are 2 ways of answering each of the 5 questions, i.e., true of false.
So, the total number of different sequences of answers `=(2xx2xx2xx2xx2)=32.`
There is only one all correct answer.
Maximum number of sequences of answers leaving aside the all correct answer `=(32-1)=31.`
Hence, the maximum possible number of students = 31.