There are 10 questions in a question paper. In how many ways, a student can solve these questions, if he solves one or more questions?

Options

A. 1024
B. 1025
C. 1023
D. 1000

Answer

To solve the problem of how many ways a student can solve one or more questions out of 10 questions in a question paper, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have 10 questions.
- The student can solve any combination of these questions, but must solve at least one question.

2. **Total Combinations**:
- For each question, the student has two choices: either to solve it or not to solve it.
- Therefore, for 10 questions, the total number of combinations (including the option of not solving any questions) is \(2^{10}\).

3. **Calculating \(2^{10}\)**:
- \(2^{10} = 1024\). This includes all possible combinations of the questions, including the scenario where no questions are solved.

4. **Excluding the Case of Solving No Questions**:
- Since the student must solve at least one question, we need to subtract the one case where no questions are solved.
- Thus, the total number of ways to solve one or more questions is \(1024 - 1 = 1023\).

5. **Final Answer**:
- Therefore, the number of ways a student can solve one or more questions from the 10 questions is **1023**.

### Summary of Steps:
1. Calculate total combinations: \(2^{10} = 1024\).
2. Subtract the case of solving no questions: \(1024 - 1 = 1023\).
3. The final answer is **1023**.