Questions in differentiation

Select	Question
	The normal to the curve $x=a\text{ }(1+\cos \theta ),\,y=a\sin \theta $ at $'\theta '$ always passes through the fixed point
	If ST and SN are the lengths of the subtangent and the subnormal at the point $\theta =\frac{\pi }{2}$ on the curve $x=a(\theta +\sin \theta ),y=a(1-\cos \theta ),a\ne 1$ , then
	The equation of the tangent to the curve $x=2{{\cos }^{3}}\theta $ and $y=3{{\sin }^{3}}\theta $ at the point $\theta =\pi /4$ is
	The curve given by $x+y={{e}^{xy}}$ has a tangent parallel to the y-axis at the point
	The value of the function $(x-1){{(x-2)}^{2}}$ at its maxima is
	The maximum and minimum values of the function $\|\sin 4x+3\|$ are
	Local maximum and local minimum values of the function $(x-1){{(x+2)}^{2}}$ are
	The function ${{x}^{5}}-5{{x}^{4}}+5{{x}^{3}}-10$ has a maximum, when x =
	The maximum value of function ${{x}^{3}}-12{{x}^{2}}+36x+$ 17 in the interval [1, 10] is
	The maximum value of the function ${{x}^{3}}+{{x}^{2}}+x-4$ is