Match each entry in List - I to the correct entries in List - II

	LIST-I		LIST-II
I)	Suppose $ABC$  is a triangle with three acute angles  $A,B\text{ and }C.$  The point whose coordinates are  $(\cos B-\sin A,\sin B-\cos A)$  can be in the	P)	1st quadrant
II)	$2^{\sin \theta }>1\text{ and }{3}^{\cos \theta }<1,\text{ then }\theta \in$	Q)	2nd quadrant
III)	For  $|\cos x+\sin x|=\left|\sin x\right|+\left|\cos x\right|,x$  belongs to	R)	3rd quadrant
IV)	If  $\sqrt{\frac{1-\sin A}{1+\sin A}}+\frac{\sin A}{\cos A}=\frac{1}{\cos A},$  for all permissible values of  $A,$ then  $A$ can belong to	S)	4th quadrant

A)  Since angles  $A,B,\text{and }C$ are acute angles, we have
 $A+B>\pi /2$
 $A>\frac{\pi }{2}-B$
 $\Rightarrow \sin A-\cos B>0$
$\Rightarrow \cos B-\sin A<0$             (i)
Again,  $B>\frac{\pi }{2}-A$
 $\sin B>\cos A$
  $\sin B-\cos A>0$               (ii)
From Eqs (i) and (ii), we get that  $x$-coordinate is  $-ve$  and  $y$-coordinate is  $+ve$
Therefore, point is in 2nd quadrant only.
B)  $2^{\sin \theta }>1\Rightarrow \sin \theta >0$ $\Rightarrow 3^{\cos \theta }<1\Rightarrow \cos \theta <0$$\Rightarrow \theta \in$  2nd or 3rd quadrant
Hence, $\theta \in$ 2nd quadrant
C)  $|\cos x+\sin x|=\left|\sin x\right|+\left|\cos x\right|$
Thus, $\cos x\text{ and }\sin x$  must have same sign or at least one is zero
So,   $x\in$ 1st or 3rd quadrant
D) $L.H.S-\frac{1-\sin A}{\left|\cos A\right|}+\frac{\sin A}{\cos A}=\frac{1}{\cos A},$   which is truly only if  $\left|\cos A\right|=\cos A$