Sets, Relations and FunctionsMCQPYQ May 18Question 1885 of 217
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The numbers of proper subset of the set (3,4,5,6,7)\displaystyle (3, 4, 5, 6, 7) is

Options

A32
B31
C30
D25
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Correct Answer

Option b31

All Options:

  • A32
  • B31
  • C30
  • D25

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Detailed Solution & Explanation

Let the given set be S={3,4,5,6,7}\displaystyle S = \{3, 4, 5, 6, 7\}.
The number of elements in the set S\displaystyle S is n=5\displaystyle n = 5.
The total number of subsets of a set with n\displaystyle n elements is given by the formula:
Total Subsets=2n\text{Total Subsets} = 2^n
Substituting n=5\displaystyle n = 5:
Total Subsets=25=32\text{Total Subsets} = 2^5 = 32
A proper subset of a set S\displaystyle S is any subset of S\displaystyle S other than S\displaystyle S itself. Therefore, the number of proper subsets is given by:
Number of Proper Subsets=2n1\text{Number of Proper Subsets} = 2^n - 1
Substituting the values:
Number of Proper Subsets=321=31\text{Number of Proper Subsets} = 32 - 1 = 31
Hence, **Option B** is the correct answer.

About This Chapter: Sets, Relations and Functions

Paper

Paper 3: Quantitative Aptitude

Weightage

3-5 Marks

Key Topics

Sets, Relations, Functions

This chapter covers Sets, Relations, Functions and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

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