Question

There are $10$ true-false questions in an examination. Then these questions can be answered in how many ways?
1. $240$ways
2. $20$ ways
3. $1024$ ways
4. $100$ways

Answer 1

Here we are given that there are true-false questions in an examination. We need to find the number of ways in which these questions can be answered. We will use the basic mathematical operations such as multiplication , exponents , etc to solve such types of problems.

Complete step-by-step solution:
Here we are given that there are true-false questions in an examination. We need to find the number of ways in which these questions can be answered. In order to solve this question firstly we should know in how many ways a single question can be answered.
We know that in a true-false type question there are only two ways to answer a question that is the answer can be either true or false. Hence each question can be answered in two ways that are either true or false.
Hence for true-false questions there are $2 \times 2 \times 2... \times 2$ ($10$ times)
Therefore, total number of ways in which these true-false questions can be answered is equal to ${2^{10}} = 1024$ways
Therefore we get our required answer.
Therefore option (3) is the correct answer.

Note: In such types of questions we should know exactly how many ways are there to perform a specific task and then extend it to solve the constituent parts. Like in this question we should know the ways in which a true-false type question can be solved and then we extend it for $10$ questions. We need to do the calculations very carefully and must recheck them as it will alter the solution if the calculations are wrong.