Electric field in a plane electromagnetic wave is given by E = 50 sin(500x $$-$$ 10 $$\times$$ 10¹⁰ t) V/m The velocity of electromagnetic wave in this medium is :

(Given C = speed of light in vacuum)

Five identical cells each of internal resistance 1$$\Omega$$ and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same?

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.


The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :

A body of mass (2M) splits into four masses (m, M $$-$$ m, m, M $$-$$ m}, which are rearranged to form a square as shown in the figure. The ratio of $${M \over m}$$ for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ............ .