In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every student is unique, then the maximum number of students who appeared for the test is \(\ldots\)
Show Hint
Total sequences 2^7 minus the one all-correct sequence.
Step 1: Count sequences by choosing positions:
A sequence is fixed by choosing which of the 7 answers are wrong. The number of wrong answers can be 0 to 7.
Step 2: Add up allowed cases:
The number of sequences with at least one wrong answer is
$\binom{7}{1} + \binom{7}{2} + \dots + \binom{7}{7} = 2^7 - \binom{7}{0} = 128 - 1 = 127$.
Step 3: Interpretation:
The case with 0 wrong answers is the single all-correct sequence, which no student has. Every other sequence can be used by exactly one student.
Final Answer:
At most 127 students, option (C).
\[ \boxed{127 \text{ (C)}} \]