Questions in trigonometry

Select	Question
	In any triangle $AB=2,BC=4,CA=3$ and D is mid point of BC, then
	If the angles of a triangle are in the ratio $4:1:1$, then the ratio of the longest side to the perimeter is
	If in any $\Delta ABC$ , $\cot \frac{A}{2},\cot \frac{B}{2},\cos \frac{C}{2}$ are in A. P. then
	The smallest angle of the $\Delta ABC$ , when $a=7,b=4\sqrt{3}$ and $c=\sqrt{13},$ is
	In a $\Delta ABC,$ if $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$ , then $\cos C=$
	In a$\Delta ABC,$ if $b=20,c=21$ and $\sin A=3/5$ , then $a=$
	Let D be the middle point of the side BC of a triangle ABC. If the triangle ADC is equilateral, then ${{a}^{2}}:{{b}^{2}}:{{c}^{2}}$ is equal to
	The ratio of the sides of triangle ABC is $1:\sqrt{3}:2$. The ratio of $A:B:C$ is
	In a triangle $ABC,\,\,b=\sqrt{3}$ , $c=1$ and $\angle A={{30}^{o}}$ , then the largest angle of the triangle is
	The lengths of the sides of a triangle are $\alpha -\beta ,\alpha +\beta $ and $\sqrt{3{{\alpha }^{2}}+{{\beta }^{2}}},$ $(\alpha >\beta >0)$. Its largest angle is