Permutations and CombinationsMCQMTP May 18Question 1722 of 251
All Questions

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

Options

A1021
B2048
C4096
DNone of these
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Correct Answer

✅ Option c — 4096

All Options:

  • A1021
  • B2048
  • C4096
  • DNone of these

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Detailed Solution & Explanation

Each of the 12\displaystyle 12 questions can be answered in 2\displaystyle 2 ways: either **Yes** or **No**.

By the fundamental multiplication principle of counting, if there are n\displaystyle n independent trials, each with p\displaystyle p outcomes, the total number of outcomes is pn\displaystyle p^n.

Here, p=2\displaystyle p = 2 and n=12\displaystyle n = 12.
Total Ways=212\text{Total Ways} = 2^{12}
Total Ways=2×2×2×2×2×2×2×2×2×2×2×2\text{Total Ways} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2
  ⟹  212=4096\implies 2^{12} = 4096

Since 4096\displaystyle 4096 is listed as **Option C**, the mathematically correct choice is Option C.

**Discrepancy Note:**
The mathematical calculation yields exactly 4096\displaystyle 4096, which corresponds to **Option C**. The textbook answer key has a typographical error in this particular version of the question, indicating **Option D** (None of these) as correct.

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! + \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.

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