The ratio of resolving powers of an optical microscope for two wavelength $$\lambda $$₁ = 4000 $$\mathop A\limits^ \circ $$ and $${\lambda _2}$$ = 6000 $$\mathop A\limits^ \circ $$ is

Figure shows a circuit that contains three identical resistors with resistance R = 9.0 $$\Omega $$ each, two identical inductors with inductance $$L$$ = 2.0 mH each, and an ideal battery with emf $$\varepsilon = 18V$$. The current $$i$$ through the battery just after the switch closed is

A long solenoid of diameter 0.1 m has 2 $$ \times $$ 10⁴ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10 $$\pi $$² $$\Omega $$, the total charge flowing through the coil during this time is

Two polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light $$I$$₀ is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle 45^o with that of P₁. The intensity of transmitted light through P₂ is