Matrix matching type questions, observe the following lists

	List – I		List – II
A)	$f\left(x\right)=x+\frac{1}{x}$is decreasing in	P)	$R$
B)	$f\left(x\right)=1-x^3$is decreasing in	Q)	$\left(O,\frac{\text{1}}{e}\right)$
C)	$f\left(x\right)=x{e}^{-x}$is decreasing in	R)	$(-1,0)\cup (0,1)$
D)	$f\left(x\right)=x^x$is decreasing in	S)	$\left(1,\infty \right)$
		T)	$\left(0,\infty \right)$

 

$\begin{array}{l}i\left)f^1\right(x)=1-\frac{1}{x^2}<0\\ x\in \left(-1,0\right)\cup \left(0,1\right)\\ ii\left)f^1\right(x)=-3x^2<0\Rightarrow x\in R\\ iii\left)f^1\right(x)=-x{e}^{-x}+e^{-x}<0\Rightarrow (1-x)e^{-x}<0(e^{-x}isalways+ve)\\ x>1\\ iv\left)f^1\right(x)=x^x(1+\log x)\Rightarrow x\in \left(0,\stackrel{\perp }{e}\right)\end{array}$