In $\triangle ABC$,if $\cot \frac{A}{2} : \cot \frac{B}{2} : \cot \frac{C}{2} = 4 : 3 : 2$,then $a : b : c =$

If in a $\triangle ABC$,$\frac{1}{a+c} + \frac{1}{b+c} = \frac{3}{a+b+c}$,then $\angle C$ is equal to (in $^{\circ}$)

In a triangle $ABC$,if $\cot \frac{A}{2} \cot \frac{B}{2} = K$,then all the possible values of $K$ lie in

Which of the following sets of data does not uniquely determine an acute-angled $\Delta ABC$ ($R$ = circum-radius)?

In a triangle $ABC$ with usual notations $a=2$ and $b=3$,the value of $\frac{\cos 2A}{a^2} - \frac{\cos 2B}{b^2}$ is:

In a triangle,the lengths of the two larger sides are $10 \, cm$ and $9 \, cm$ respectively. If the angles of the triangle are in $A.P.$,then the length of the third side in $cm$ can be