In $\Delta ABC$ with usual notations $a=4, b=3, \angle A=60^{\circ}$,then $c$ is a root of the equation

In a triangle $ABC$ with usual notations,if $\angle A = 30^{\circ}$,then the value of $\left(1+\frac{a}{c}+\frac{b}{c}\right)\left(1+\frac{c}{b}-\frac{a}{b}\right)=$

In $\triangle ABC$,with usual notations,if $\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c}$,then $m \angle C$ is equal to

Assertion $(A)$: In $\triangle ABC$,if $r=6, r_2=36, R=15$,then $c^2+a^2=b^2$.
Reason $(R)$: In $\triangle ABC$,if $r:R:r_2=1:2.5:6$,then $B=90^{\circ}$.
The correct option among the following is:

If in a $\Delta ABC$,the altitudes from the vertices $A, B, C$ on opposite sides are in $H.P.$,then $\sin A, \sin B, \sin C$ are in

In a $\triangle ABC$,$\cot A+\cot B+\cot C=$