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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2015 · Mathematics · Permutation and Combination

A polygon has 44 diagonals. The number of its sides is

A polygon has 44 diagonals. The number of its sides is

Options

  1. A11
  2. B10
  3. C8
  4. D7

Correct answer

A. 11

Step-by-step solution

No. of diagonals in a polygen =nC2−n={ }^n C_2-n⇒44=nC2−n⇒44=n!2!(n−2)!−n⇒44=n(n−1)2−n⇒44=n(n−3)2⇒n2−3n−88=0⇒(n−11)(n+8)=0n≠−8n=11\begin{aligned} & \Rightarrow \quad 44={ }^{\mathrm{n}} \mathrm{C}_2-\mathrm{n} \\ & \Rightarrow \quad 44=\frac{\mathrm{n}!}{2!(\mathrm{n}-2)!}-\mathrm{n} \\ & \Rightarrow \quad 44=\frac{\mathrm{n}(\mathrm{n}-1)}{2}-\mathrm{n} \\ & \Rightarrow \quad 44=\frac{\mathrm{n}(\mathrm{n}-3)}{2} \\ & \Rightarrow \quad \mathrm{n}^2-3 \mathrm{n}-88=0 \\ & \Rightarrow \quad(\mathrm{n}-11)(\mathrm{n}+8)=0 \\ & \mathrm{n} \neq-8 \\ & \mathrm{n}=11 \end{aligned}$$
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