A system of three polarizers P₁, P₂, P₃ is set up such that the pass axis of P₃ is crossed with respect to that of P₁. The pass axis of P₂ is inclined at 60^o to the pass axis of P₃. When a beam of unpolarized light of intensity I0 is incident on P₁, the intensity of light transmitted by the three polarizers is I. The ratio ($${{{I_0}} \over I}$$) equals (nearly) :

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $$\rho $$(r) = kr, where r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite points, at equal distance, $$a$$ from the centre. If A and B do not experience any force, then :

Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and t = $${L \over R}$$ is :

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $$\mathop A\limits^o $$). The de-Broglie wavelength of this electron is :