Match the values of $\frac{d y}{d x}$ at $x=\frac{\pi}{3}$ for the following system of curves in parametric form given in List-I with those of the items in List-II
List-I List-II (i) x = a ( θ − sin θ ) , y = a ( 1 − cos θ ) x = a ( θ − sin θ ) , y = a ( 1 − cos θ ) x=a(theta-sin theta),y=a(1-cos theta) (a) 4 3 4 3 4sqrt3 (ii) x = 3 cos θ − 2 cos 3 θ , y = 3 sin θ − 2 sin 3 θ x = 3 cos θ − 2 cos 3 θ , y = 3 sin θ − 2 sin 3 θ x=3cos theta-2cos^(3)theta,y=3sin theta-2sin^(3)theta (b) − 1 3 3 − 1 3 3 (-1)/(3sqrt3) (iii) x = 3 cos θ − cos 3 θ , y = 3 sin θ − sin 3 θ x = 3 cos θ − cos 3 θ , y = 3 sin θ − sin 3 θ x=3cos theta-cos^(3)theta,y=3sin theta-sin^(3)theta (c) 3 3 sqrt3 (iv) x = a log sin θ , y = a tan θ x = a log sin θ , y = a tan θ x=a log sin theta,y=a tan theta (d) 1 3 1 3 (1)/(sqrt3) (e) 1 3 3 1 3 3 (1)/(3sqrt3)
