An electron (mass m) with initial velocity $$\overrightarrow v = {v_0}\widehat i + {v_0}\widehat j$$ is in an electric field $$\overrightarrow E = - {E_0}\widehat k$$. If $$\lambda _0$$ is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

Consider two charged metallic spheres S₁ and S₂ of radii R₁ and R₂, respectively. The electric fields E₁ (on S₁) and E₂ (on S₂) on their surfaces are such that E₁/E₂ = R₁/R₂. Then the ratio V₁ (on S₁) / V₂ (on S₂) of the electrostatic potentials on each sphere is :

A particle moves such that its position vector $$\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j$$ where $$\omega $$ is a constant and t is time. Then which of the following statements is true for the velocity $$\overrightarrow v \left( t \right)$$ and acceleration $$\overrightarrow a \left( t \right)$$ of the particle :

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by :
(Graphs are drawn schematically and are not to scale)