Permutations and CombinationsMCQMTP June 24 Series IIIQuestion 1748 of 251

There $\displaystyle 12$ questions to be answered to be Yes or No. How many ways this can be answered

Options

\displaystyle 1021

\displaystyle 2048

\displaystyle 4096

DNone of these

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Correct Answer

✅ Option c — $\displaystyle 4096$

All Options:

A $\displaystyle 1021$
B $\displaystyle 2048$
C $\displaystyle 4096$
DNone of these

Detailed Solution & Explanation

Each of the

\displaystyle 12

questions can be answered in

\displaystyle 2

ways: either **Yes** or **No**.

By the fundamental multiplication principle of counting, the number of ways to answer all

\displaystyle 12

questions is:

\text{Total Ways} = \underbrace{2 \times 2 \times \dots \times 2}_{12 \text{ times}} = 2^{12}

Let us calculate

\displaystyle 2^{12}

2^{12} = 4096

Hence, **Option C** is the correct answer.

About This Chapter: Permutations and Combinations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Factorials, Permutations, Combinations

This chapter deals with the fundamental principles of counting. It covers factorials, circular permutations, restricted permutations, combinations, and the differences between selecting items versus arranging them.

View Official ICAI Syllabus

Exam Strategy Tip

The most common mistake is confusing 'P' (Arrangement) with 'C' (Selection). If order matters (like opening a lock), use P. If order doesn't matter (like choosing a team), use C.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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There 12\displaystyle 1212 questions to be answered to be Yes or No. How many ways this can be answered