JEE Main20257 Apr 2025Evening ShiftMathematicsPermutation and CombinationActual
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 x^2 16 + y^2 n =1 is :
Options
- A3 4
- B1 2
- C7 4
- D1 2
Correct answer
D. 1 2
Step-by-step solution
aligned & Total trangles = = ^ h C ₃ & Total auadrilaterals = ^ h C ₄= q & ^ n C ₃+ ^ n C ₄=126 ^ n +1 C ₄=126 & n +1=9 n =8 & x ^2 16 + y ^2 n =1 x ^2 16 + y ^2 8 =1 & e = 1- 8 16 = 8 16 = 1 2 aligned