JEE Advanced 2020 Full Test 6 Paper 2

Set f(x)=ax4+bx3+cx2+dx+e,a≠0, is a function such that x=1,x=2 and x=3 are normals to the curve y=f(x) such that f(2) is always greater than f(0), then which of the following are true for f(x)
(i) f(x) has 2 local maxima
(ii) There exist only one value of k such that Rolle's theorem is applicable to f(x) on the interval [0,k]
(iii) f(x)=0 has two imaginary roots.