The number of all the possible selections which a student can make for answering one or more questions out of 10 given questions in a paper, when each question has an alternative is :

Options

A. 1345
B. 23560
C. 541340
D. 59048

Answer

To solve the problem of determining the number of possible selections a student can make for answering one or more questions out of 10 given questions, where each question has an alternative, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Choices for Each Question**:
Each question has three possible choices:
- Answer the main part of the question (let's call this choice A).
- Answer the alternative part of the question (let's call this choice B).
- Do not answer the question at all (which we will exclude later).

2. **Calculating Total Choices for All Questions**:
Since there are 10 questions and each question has 3 choices, the total number of ways to choose answers for all questions is given by:
\[ \text{Total Choices} = 3^{10} \]

3. **Calculating \(3^{10}\)**:
Now, we calculate \(3^{10}\):
\[ 3^{10} = 59049 \]

4. **Excluding the Case of Not Answering Any Question**:
However, the problem states that the student must answer at least one question. The only case we need to exclude is when the student chooses not to answer any of the questions at all. This is one specific case (choosing not to answer for all 10 questions).

5. **Final Calculation**:
To find the total number of valid selections (where at least one question is answered), we subtract the one case where no questions are answered from the total choices:
\[ \text{Valid Selections} = 59049 - 1 = 59048 \]

6. **Conclusion**:
Therefore, the total number of possible selections the student can make for answering one or more questions is:
\[ \boxed{59048} \]