JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by joining the vertices of \(P\). If \(p+q=126\), then the eccentricity of the ellipse \(\frac{x^2}{16}+\frac{y^2}{n}=1\) is :
- A \(\frac{3}{4}\)
- B \(\frac{1}{2}\)
- C \(\frac{\sqrt{7}}{4}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Total trangles }=\Rightarrow={ }^{\mathrm{h}} \mathrm{C}_3 \\ & \text { Total auadrilaterals }={ }^{\mathrm{h}} \mathrm{C}_4=\mathrm{q} \\ & { }^{\mathrm{n}} \mathrm{C}_3+{ }^{\mathrm{n}} \mathrm{C}_4=126 \Rightarrow{ }^{\mathrm{n}+1} \mathrm{C}_4=126…
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