Questions in differentiation

Select	Question
	Let $f\,(x)=1+2{{x}^{2}}+{{2}^{2}}{{x}^{4}}+.....+{{2}^{10}}{{x}^{20}}$ , then $f(x)$ has
	Area of the greatest rectangle that can be inscribed in the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$ is
	The function $x+\frac{1}{x},(x\ne 0)$is a non-increasing function in the interval
	The function $\frac{1}{1+{{x}^{2}}}$is decreasing in the interval
	Which of the following is not a decreasing function on the interval $\left( 0,\frac{\pi }{2} \right)$
	The function $\frac{x-2}{x+1},(x\ne -1)$is increasing on the interval
	In the interval [0, 1], the function ${{x}^{2}}-x+1$is
	The interval in which the function ${{x}^{2}}{{e}^{-x}}$is non decreasing, is
	On the interval $\left( 0,\frac{\pi }{2} \right)$, the function log sin x is
	The function $\sin x-\cos x$is increasing in the interval