In triangle $ABC$,$a=2$,$b=3$ and $\sin A=\frac{2}{3}$,then $B$ is equal to (in $^{\circ}$)

In a $\Delta ABC$,the expression $\left( \frac{a^2}{\sin A} + \frac{b^2}{\sin B} + \frac{c^2}{\sin C} \right) \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$ simplifies to,where $\Delta$ is the area of the triangle.

In a $\triangle ABC$,if $\angle A = 60^{\circ}$,then $\frac{b}{c+a} + \frac{c}{a+b} = $

In a $\Delta PQR$,if $3 \sin P + 4 \cos Q = 6$ and $4 \sin Q + 3 \cos P = 1$,then the angle $R$ is equal to:

In $\Delta ABC,\, \left( {\cot \frac{A}{2} + \cot \frac{B}{2}} \right)\,\left( {a{{\sin }^2}\frac{B}{2} + b{{\sin }^2}\frac{A}{2}} \right) =$

If $b = 3, c = 4$ and $B = \frac{\pi}{3}$,then the number of triangles that can be constructed is