A complex number z is said to be unimodular if $$\,\left| z \right| = 1$$. Suppose $${z_1}$$ and $${z_2}$$ are complex numbers such that $${{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}$$ is unimodular and $${z_2}$$ is not unimodular. Then the point $${z_1}$$ lies on a :

Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

A red $$LED$$ emits light at $$0.1$$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $$1$$ $$m$$ from the diode is :