A set of 6 questions contains true / false type questions . Maximum how many students can take the test if all the students answer different from others and must attempt all the questions ?

Answer

To solve the problem of how many students can take a test consisting of 6 true/false questions, where each student must answer differently, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Question**: We have a set of 6 questions, and each question can be answered in two ways: True (T) or False (F). We need to determine the maximum number of students who can take the test such that each student's answers are unique.

2. **Calculating the Number of Combinations**: For each of the 6 questions, there are 2 possible answers (T or F). Therefore, the total number of unique combinations of answers for all 6 questions can be calculated using the formula for combinations:
\[ \text{Total Combinations} = 2^{\text{Number of Questions}} = 2^6 \]

3. **Performing the Calculation**:
\[ 2^6 = 64 \]
This means there are 64 different ways to answer the 6 questions.

4. **Conclusion**: Since each student must have a unique set of answers, the maximum number of students that can take the test, each with different answers, is equal to the total number of unique combinations calculated. Thus, the maximum number of students is:
\[ \text{Maximum Students} = 64 \]

### Final Answer:
The maximum number of students that can take the test is **64**.

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