If in a $\triangle ABC$,$r_1=2$,$r_2=3$ and $r_3=6$,then $a$ equals to

If the points with position vectors $60 \hat{i}+3 \hat{j}$,$40 \hat{i}-8 \hat{j}$,and $a \hat{i}-52 \hat{j}$ are collinear,then $a$ is equal to

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centered cubic,and face-centered cubic,then the ratio of radii of the spheres in these systems will be respectively:

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

If $X$ is a Poisson variate such that $\alpha = P(X=1) = P(X=2)$,then $P(X=4)$ is equal to