Question

There are 8 true/false questions in an examination. The number of ways in which this question can be answered, is
(a) 256
(b) 1024
(c) 16
(d) 64

Answer 1

Hint: First, before proceeding for this, we must know that the examination has the question in which there are two options which are true or false. Then, have the number of ways for a single question to select the answer as 2 which is true or false. Then, similarly we can clearly see that the condition says that we are having 8 questions in the exam with the same pattern to answer in either true or false.

Complete step-by-step answer:
In this question, we are supposed to find the number of ways in which this question can be answered when there are 8 true/false questions in an examination.
So, before proceeding for this, we must know that the examination has the question in which there are two options which are true or false.
So, we have the number of ways for a single question to select the answer as 2 which is true or false.
Similarly, if the question count is increased to two then the number of ways for the answer to be given becomes as:
$2\times 2$
So, by solving this we get the number of ways for two questions as:
4
Then, similarly we can clearly see that the condition says that we are having 8 questions in the exam with the same pattern to answer in either true or false.
So, we get the expression for the number of ways to answer the question in either true or false for 8 questions as:
$2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
Now, b y solving the above expression, we get the number of ways as:
${{2}^{8}}=256$
So, we get the number of ways in which this question can be answered when there are 8 true/false questions in an examination as 256.

So, the correct answer is “Option A”.

Note: Now, to solve these type of the questions we need to be careful while solving the power or exponents as sometimes we take ${{3}^{2}}$ as multiplication of 3 and 2 which gives 6 and it is the wrong answer as ${{3}^{2}}$actually means multiplication of 3 two times which gives 9 as correct answer.