JEE Advanced Model Paper 10 with solutions for online practice

By L.M.V.T., we get
f(1) - f(0) = f'(C1) , 0 < C1 < 1
and f(2) - f(1) = f'(C2) , 1 < C2 < 2
By subtraction :
f(2) + f(0) - 2f(1) = f'(C2) - f'(C1)
= (C2−C1) f''(C)
∵ C1 < C < C2 ⇒ f(0) + f(2) - 2f(1) < 0
∴ f(0) + f(2) < 2f(1)
∴ Major axis of ellipse coincide with y-axis
∴ Eccentricity of ellipse = √1−

f(0)+f(2)

2f(1)