AIEEE 2012 PYQ Mock Test

An object $2.4\text{m}$ in front of a lens forms a sharp image on a film $12\text{cm}$ behind the lens. A glass plate $1\text{cm}$ thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?

A diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ($n$ is an integer):

A spectrometer gives the following reading when used to measure the angle of a prism.Main scale reading: $58.5$ degreeVernier scale reading: $09$ divisionsGiven that $1$ division on main scale corresponds to $0.5$ degree. Total divisions on the vernier scale is $30$ and match with $29$ divisions of the main scale. The angle of the prism from the above data is:

Statement 1: When a charge $q$ is taken from the centre to the surface of an insulating solid sphere of radius $R$ and uniform charge density $\rho$, its potential energy changes by $\frac{q\rho R^2}{3{ϵ}_0}$.Statement 2: The electric field at a distance $r(r<R)$ from the centre of the sphere is $\frac{\rho r}{3{ϵ}_0}$.

Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p$, $r_d$ and $r_{\alpha }$. Which one of the following relations is correct?