AP EAMCET · Maths · Permutation Combination
A polygon has 54 diagonals. Then, the number of its sides is
- A 7
- B 9
- C 10
- D 12
Answer & Solution
Correct Answer
(D) 12
Step-by-step Solution
Detailed explanation
Number of diagonals in polygon \(=54\) Let the number of sides in polygon \(=n\) Then, The number of diagonal in any polygon \(=\frac{n(n-3)}{2}\) \(54=\frac{n(n-3)}{2}\) \(n^2-3 n=108\) \(n^2-3 n-108=0\) \(n^2-12 n+9 n-108=0\) \(n(n-12)+9(n-12)=0\) \((n+9)(n-12)=0\) \(n=-9\) or…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let be defined on by , thenAP EAMCET 2018 Medium
- \(\int \frac{x^3-x^2+x-1}{x-1} d x\) is equal toAP EAMCET 2021 Easy
- The harmonic conjugate of \((2,3,4)\) with respect to the points \((3,-2,2),(6,-17,-4)\) isAP EAMCET 2016 Medium
- The incentre of triangle formed by the lines \(x+y=1, x=1, y=1\) isAP EAMCET 2020 Hard
- In a \(\triangle A B C, \angle C=60^{\circ}\) and \(\angle A=75^{\circ}\). If \(D\) is a point on \(A C\) such that the area of \(\triangle B A D\) is \(\sqrt{3}\) times the area of \(\triangle B C D\), then the measure of \(\angle A B D\) isAP EAMCET 2020 Easy
- If -coordinate of a point on the line joining the points and is , then the -coordinate ofAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- \(\int(1-\cos x) \operatorname{cosec}^2 x d x\) is equal toAP EAMCET 2021 Medium
- The correct statement about the product of the following reaction is
\(\mathrm{CH}_3 \mathrm{CHO} \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{O}]{\text { (i) } \mathrm{C}_2 \mathrm{H}_5 \mathrm{MgBr}}\) productAP EAMCET 2025 Medium - The area (in sq units) of the quadrilateral formed by two pairs of lines \(\lambda^2 x^2-m^2 y^2-n(\lambda x+m y)=0 \quad\) and \(\lambda^2 x^2-m^2 y^2+n(\lambda x+m y)=0\) is:AP EAMCET 2003 Hard
- A particle is executing simple harmonic motion with a time period of 3 s . At a position where the displacement of the particle is \(60 \%\) of its amplitude, the ratio of the kinetic and potential energies of the particle isAP EAMCET 2024 Easy
- Three rods \(A B, B C\) and \(B D\) made of the same material and having the same cross-section have been joined as shown in the figure.
The ends \(A, C\) and \(D\) are held at temperatures of \(20^{\circ} \mathrm{C}, 80^{\circ} \mathrm{C}\) and \(80^{\circ} \mathrm{C}\) respectively. If each rod is of same length, then the temperature at the junction \(B\) of the three rods isAP EAMCET 2010 Easy - The area (in sq. units) bounded by the curve and the tangent to it at and the -axis isAP EAMCET 2019 Easy