In any $\Delta ABC$,if $a \cos B = b \cos A$,then the triangle is

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

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:

In a triangle $ABC$,if $A = 2B$ and the sides opposite to the angles $A, B, C$ are $\alpha + 1, \alpha - 1$ and $\alpha$ respectively,then $\alpha =$

If in $\triangle ABC$,$B=45^{\circ}$,$a=2(\sqrt{3}+1)$ and the area of $\triangle ABC$ is $6+2\sqrt{3}$ sq. units,then the side $b=$

In $\triangle ABC$, with usual notations, $(a + b + c)(b + c - a)(c + a - b)(a + b - c) = 3b^2c^2$, then $\angle A = $