The amplitude of wave disturbance propagating in the positive x-direction is given by $$y = {1 \over {{{(1 + x)}^2}}}$$ at time t = 0 and $$y = {1 \over {1 + {{(x - 2)}^2}}}$$ at t = 1 s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___________ m/s.

In an LCR series circuit, an inductor 30 mH and a resistor 1 $$\Omega$$ are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for which, the current leads the voltage by 45$$^\circ$$ is $${1 \over x} \times {10^{ - 3}}$$ F. Then the value of x is ____________.

A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses $$\left( {{m \over M}} \right)$$ is $${1 \over x}$$. The value of 'x' will be ____________.

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ___________ $$\pi$$J.