Permutations and CombinationsMCQMTP June 24 Series IIIQuestion 1748 of 249
All Questions

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

Select Your Answer (Keyboard: A, B, C, D)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $4096$

All Options:

  • A$1021$
  • B$2048$
  • C$4096$
  • DNone of these

Detailed Solution & Explanation

Each of the $12$ questions can be answered in $2\displaystyle ways: either **Yes** or **No**.<br><br>By the fundamental multiplication principle of counting, the number of ways to answer all &#36;12 questions is:
Total Ways=2×2×⋯×2⏟12 times=212\displaystyle \text{Total Ways} = \underbrace{2 ×\displaystyle \times 2 ×\displaystyle \times \dots ×\displaystyle \times 2}_{12  times\displaystyle \text{ times}} = 2^{12}
Let us calculate 212\displaystyle 2^{12}:
212=40962^{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

More Questions from Permutations and Combinations

The value of N\displaystyle N in N!+17!=18!\displaystyle N! + \displaystyle \frac{1}{7!} = \frac{1}{8!} is

A person can go from place 'A' to 'B' by 11 different modes of transport but is allowed to return to 'A' by any mode other than the one earlier. The number of different ways in which the entire journey can be completed is:

If a man travels from place A to B in 10 ways then by how many ways can he come back by another train?

If n!10(n−1)!=(n−1)!(n−3)!\displaystyle \frac{n!}{10(n-1)!} = \frac{(n-1)!}{(n-3)!} find 'n'.

Which of the following is a correct statement.

nP3=2⋅nP2\displaystyle ^nP_3 = 2 \cdot ^nP_2. Find n\displaystyle n.

Ready to Master Permutations and Combinations?

Practice all 249 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free