With usual notations,if the angles $A, B, C$ of a $\triangle ABC$ are in $A$.$P$. and $b:c = \sqrt{3}:\sqrt{2}$,then $\angle A=$ (in $^{\circ}$)

In a triangle,if the ex-radii $r_1, r_2, r_3$ are in the ratio $1: 2: 3$,then its sides are in the ratio

In a triangle $ABC$,if $A=30^{\circ}$ and $\frac{b}{(\sqrt{3}+1)^2+2(\sqrt{2}-1)}=\frac{c}{(\sqrt{3}+1)^2-2(\sqrt{2}-1)}$,then $B=$ (in $^{\circ}$)

In any $\triangle ABC$,$\frac{\cos 2A}{a^2} - \frac{\cos 2B}{b^2} =$

In $\triangle ABC$,if $a=2(\sqrt{3}+1)$,$B=45^{\circ}$ and $C=60^{\circ}$,then the area (in sq.units) of that triangle is

In a $\Delta ABC$,if two sides $b$ and $c$ and an angle $B$ are given.
Statement $-1$: Let $b = 5 \ cm, c = 3 \ cm$ and $\angle B = 60^\circ$. The total number of possible triangles is $2$.
Statement $-2$: If $c \sin B < b < c$ and $B$ is an acute angle,then there are two possible values of $\angle C$.