There are 11 True or False type questions in a test. Each question can be answered independently as either True or False. In how many different ways can a student answer all the 11 questions?

Introduction / Context:
This is a basic question from the topic of counting and binary choices. Each True or False question represents a binary decision, and the total number of different answer patterns for the whole test can be calculated using powers of 2. Such problems help develop comfort with the idea that each independent yes or no type choice doubles the number of possible outcomes.

Given Data / Assumptions:

• There are 11 questions in total.
• Each question can be answered in exactly two ways: True or False.
• Answers to different questions are independent of one another.
• We need the number of complete answer sheets possible for all 11 questions together.

Concept / Approach:
Because each question has 2 possible responses and the choices across questions are independent, we use the rule for the product of independent choices. If there are n independent binary choices, the total number of possible outcome patterns is 2^n. Here, n is 11. We do not care about correctness of the answers, only distinct answer combinations.

Step-by-Step Solution:
Step 1: For question 1, there are 2 choices: True or False.Step 2: For question 2, there are again 2 choices, independent of question 1.Step 3: This pattern continues for all 11 questions, each contributing a factor of 2.Step 4: Therefore, the total number of different answer patterns is 2 × 2 × ... (11 times) = 2^11.Step 5: Compute 2^10 = 1024 and then multiply by 2 to get 2^11 = 2048.
Verification / Alternative check:
Another way to see this is to write the answer pattern as a string of length 11, where each position can be T or F. For each of the 11 positions we have 2 possibilities, and so the total number of distinct strings is 2^11, exactly the same reasoning as above. Calculating 2^11 gives 2048, confirming our result.

Why Other Options Are Wrong:
11!/2 and 11! count permutations of 11 distinct objects, which is not relevant here because questions are fixed and answers are only two types. 1024 corresponds to 2^10, which would be correct if there were only 10 questions. Therefore 2048 is the only correct choice among the options.

Common Pitfalls:
Students sometimes confuse factorial with powers and mistakenly think that the number of ways to answer n questions is n! rather than 2^n. Another common error is miscomputing 2^11, for example stopping at 1024 and forgetting to multiply by 2 one more time. Always remember that each independent binary choice multiplies the total by 2.

Final Answer:
The number of different ways to answer the 11 True or False questions is 2048.