Each of the four inequalties given below defines a region in the $$xy$$ plane. One of these four regions does not have the following property. For any two points $$\left( {{x_1},{y_1}} \right)$$ and $$\left( {{x_2},{y_2}} \right)$$ in the region, the point $$\left( {{{{x_1} + {x_2}} \over 2},{{{y_1} + {y_2}} \over 2}} \right)$$ is also in the region. The inequality defining this region is

Suppose that the normals drawn at three different points on the parabola $${y^2} = 4x$$ pass through the point $$(h, k)$$. Show that $$h>2$$.

Let $$y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$$. Find $${{dy} \over {dx}}$$

Let the angles $$A, B, C$$ of a triangle $$ABC$$ be in A.P. and let $$b:c = \sqrt 3 :\sqrt 2 $$. Find the angle $$A$$.