Questions in differentiation

Select	Question
	If the function $f(x)=\frac{K\sin x+2\cos x}{\sin x+\cos x}$is increasing for all values of x, then
	The value of ‘a’ in order that $f(x)=\sqrt{3}$ $\sin x-\cos x-2ax+b$ decreases for all real values of x, is given by
	The interval in which the function ${{x}^{3}}$increases less rapidly than$6{{x}^{2}}+15x+5$, is
	The values of ‘a’ for which the function $(a+2){{x}^{3}}-3a{{x}^{2}}+9ax-1$ decreases monotonically throughout for all real x, are
	If $f(x)=2x+{{\cot }^{-1}}x+\log (\sqrt{1+{{x}^{2}}}-x)$, then $f(x)$
	For all real values of x, increasing function f(x) is
	The least value of k for which the function ${{x}^{2}}+kx+1$is an increasing function in the interval $1 < x < 2$is
	The interval of the decreasing function $f(x)={{x}^{3}}-{{x}^{2}}-x-4$is
	The function $f(x)={{x}^{3}}-3{{x}^{2}}-24x+5$ is an increasing function in the interval given below
	Which one is the correct statement about the function $f(x)=\sin 2x$