$$\mathrm{I_{CM}}$$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $$\mathrm{I_{AB}}$$ is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $$\frac{2}{3}$$R from center. Where R is the radius of the disc. The ratio of $$\mathrm{I_{AB}}$$ and $$\mathrm{I_{CM}}$$ is $$x:9$$. The value of $$x$$ is _____________.

An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle $$\theta$$ (as shown in figure) between the direction of force and horizontal varies as $$\theta=\mathrm{k}x$$, where k is a constant and $$x$$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $$E = {n \over k}\sin \theta $$. The value of n is ___________.

A ray of light is incident from air on a glass plate having thickness $$\sqrt3$$ cm and refractive index $$\sqrt2$$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____________ $$\times$$ 10$$^{-2}$$ cm. (given $$\sin 15^\circ = 0.26$$)

The wavelength of the radiation emitted is $$\lambda_0$$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will $$\frac{20}{x}\lambda_0$$. The value of $$x$$ is _____________.