If 'I' is moment of inertia of a thin circular disc about an axis passing through the tangent of the disc and in the plane of disc. The moment of inertia of same circular disc about an axis perpendicular to plane and passing through its centre is

A parallel plate capacitor has plate area '$$\mathrm{A}$$' and separation between plates is '$$d$$'. It is charged to a potential difference of $$\mathrm{V}_0$$ volt. The charging battery is then disconnected and plates are pulled apart three times the initial distance. The work done to increase the distance between the plates is $$\left(\varepsilon_0=\right.$$ permittivity of free space)

The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number $$\mathrm{z}$$. The value of $$\mathrm{z}$$ is

If the length of stretched string is reduced by $$40 \%$$ and tension is increased by $$44 \%$$ then the ratio of final to initial frequencies of stretched string is