In a triangle $ABC$,with usual notations,if $b=\sqrt{3}, c=1, \angle A=30^{\circ}$,then angle $B$ is (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 $PQR$,let $\angle PQR = 30^{\circ}$ and the sides $PQ$ and $QR$ have lengths $10\sqrt{3}$ and $10$,respectively. Then,which of the following statement$(s)$ is (are) $TRUE$?
$(A)$ $\angle QPR = 45^{\circ}$
$(B)$ The area of the triangle $PQR$ is $25\sqrt{3}$ and $\angle QRP = 120^{\circ}$
$(C)$ The radius of the incircle of the triangle $PQR$ is $10\sqrt{3} - 15$
$(D)$ The area of the circumcircle of the triangle $PQR$ is $100\pi$

In a $\triangle ABC$,if $r_1 = 2r_2 = 3r_3$,then $a : b =$

With usual notations,if the lengths of the sides of a triangle are $7 \text{ cm}$,$4\sqrt{3} \text{ cm}$,and $\sqrt{13} \text{ cm}$,then the measure of the smallest angle is

In $\triangle ABC$,if $8R^2 = a^2 + b^2 + c^2$,then the triangle is a/an