The mass of product liberated on anode in an electrochemical cell depends on (where $$t$$ is the time period for which the current is passed).

A wave $$y=a$$ $$\sin \left( {\omega t - kx} \right)$$ on a string meets with another wave producing a node at $$x=0.$$ Then the equation of the unknown wave is

If in the circuit, power dissipation is $$150W,$$ then $$R$$ is

Two identical particles move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of center of mass is