Question

In how many ways can a six question true and false exam be answered ?

Answer 1

Hint: In this question, the ways of answering to be determined are of true or false question. Try to first find how many ways one true or false question can be answered. Then try to find how many ways two questions can be answered. You will find a pattern in these two and try to apply the same for 6 questions.

Complete step by step answer:
We will try to start the solution by a little logic. We know that in a true or false question we have the options to answer the questions i.e. true and false. And the answer can be either true or false. Hence one question can have two answers.Similarly if we get two questions we will have two options for the first question and two options for the second question.

That is a total 4 options in total.Hence if we have been given 6 questions, each question will have two options.Hence the total options for six questions can be written as $2.2.2.2.2.2 = {2^6}$.Hence expanding it we get total options as 64.

Hence we get that 64 options will be available for 6 questions and hence 6 questions of true or false can be answered in 64 ways.

Note:Using the above mentioned logic we can find the value for n questions. That is if n true or false questions are given we can generalize the above formula and get that ${2^n}$ possible values of n questions. The value of n can be substituted and the answer for the desired number of questions can be obtained.