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 :

A ball is spun with angular acceleration $$\alpha$$ = 6t^{2} $$-$$ 2t where t is in second and $$\alpha$$ is in rads^{$$-$$2}. At t = 0, the ball has angular velocity of 10 rads^{$$-$$1} and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms^{$$-$$1} enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = $$-$$kx where k = 12 Nm^{$$-$$1}. The speed of the block as it just crosses the rough surface will be :