Problem $1$

Let $C$ be the curve given by the parametric equations

$x=cos,y=2sin2on[0,2)$

Let $m$ be the number of points on the curve at which the tangent line is horizontal, and $n$ be the number of points on the curve at which the tangent line is vertical. Then

a$.,m=4$ and $n=2$

b$.,m=2$ and $n=4$

c$.m=4$ and $n=0$

d$.m=0$ and $n=4$

e$.m=2$ and $n=0$