Sum of squares of modulus of all the complex numbers z satisfying $$\overline z = i{z^2} + {z^2} - z$$ is equal to ___________.

Let S = {1, 2, 3, 4}. Then the number of elements in the set { f : S $$\times$$ S $$\to$$ S : f is onto and f (a, b) = f (b, a) $$\ge$$ a $$\forall$$ (a, b) $$\in$$ S $$\times$$ S } is ______________.

The maximum number of compound propositions, out of p$$\vee$$r$$\vee$$s, p$$\vee$$r$$\vee$$$$\sim$$s, p$$\vee$$$$\sim$$q$$\vee$$s, $$\sim$$p$$\vee$$$$\sim$$r$$\vee$$s, $$\sim$$p$$\vee$$$$\sim$$r$$\vee$$$$\sim$$s, $$\sim$$p$$\vee$$q$$\vee$$$$\sim$$s, q$$\vee$$r$$\vee$$$$\sim$$s, q$$\vee$$$$\sim$$r$$\vee$$$$\sim$$s, $$\sim$$p$$\vee$$$$\sim$$q$$\vee$$$$\sim$$s that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to __________.

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $${v_2} = {n \over {{m^2}}}{v_1}$$ and $${a_2} = {{{a_1}} \over {mn}}$$ respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :