A transparent cube of side, made of a material of refractive index $$\mu $$₂, is immersed in a liquid of refractive index $$\mu $$₁($$\mu $$₁ < $$\mu $$₂). A ray is incident on the face AB at an angle $$\theta $$(shown in the figure). Total internal reflection takes place at point E on the face BC.
Then $$\theta $$ must satisfy :

A particle is moving with speed v = b$$\sqrt x $$ along positive x-axis. Calculate the speed of the particle at time t = $$\tau $$(assume that the particle is at origin t = 0)

In the given circuit, the charge on 4 $$\mu $$F capacitor will be :

Figure shows a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6V. If the unregulated input voltage varies between 10 V to 16 V, then what is maximum Zener current?