Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2015 · Mathematics · Permutation and Combination

Let A=\ 1,2,3,4,5,6,7,8,9,10\ . Then the number of subsets of A...

Let A={1,2,3,4,5,6,7,8,9,10}A=\{1,2,3,4,5,6,7,8,9,10\}. Then the number of subsets of A containing exactly two elements is

Options

  1. A20
  2. B40
  3. C45
  4. D90

Correct answer

C. 45

Step-by-step solution

A={1,2,3,4,5,6,7,8,9,10}A=\{1,2,3,4,5,6,7,8,9,10\} Number of subsets of A containing two elements =9+8+7+6+5+4+3+2+19(9+1)2=902=45\begin{aligned} & =9+8+7+6+5+4+3+2+1 \\ & \frac{9(9+1)}{2}=\frac{90}{2}=45 \end{aligned}\therefore \quadOption(C)iscorrectAlternateMethodThenumberofsubsetsofAcontainingexactlytwoelementsis:Option (C) is correct Alternate Method The number of subsets of A containing exactly two elements is:{ }^{10} \mathrm{C}_2=\frac{10 \times 9}{2 \times 1}=45$
Practice Permutation and Combination on Quantrex Academy →

More from Permutation and Combination

All Permutation and Combination questions Full Permutation and Combination list Permutation and Combination JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs