There are 10 true - false statements in a question paper. How many sequences of answers are possible ?

Answer

To solve the problem of how many sequences of answers are possible for 10 true-false statements, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have 10 statements, and each statement can be answered in one of two ways: True (T) or False (F).

2. **Identifying Choices for Each Statement**:
- For each of the 10 statements, there are 2 choices: T or F.

3. **Calculating Total Sequences**:
- Since the choices for each statement are independent of each other, we can use the multiplication principle of counting.
- For the first statement, there are 2 choices.
- For the second statement, there are also 2 choices.
- This continues for all 10 statements.

4. **Using Exponents**:
- The total number of sequences can be calculated as:
\[ \text{Total sequences} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{10} \]

5. **Calculating \(2^{10}\)**:
- Now, we compute \(2^{10}\):
\[ 2^{10} = 1024 \]

6. **Final Answer**:
- Therefore, the total number of sequences of answers possible for the 10 true-false statements is **1024**.