The entropy of any system is given by
$$S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right]$$ where $$\alpha$$ and $$\beta$$ are the constants. $$\mu$$, J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively.
[Take $$S = {{dQ} \over T}$$]
Choose the incorrect option from the following :

AC voltage V(t) = 20 sin$$\omega$$t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the area is 1 m². The amplitude of the oscillating displacement current for the applied AC voltage is _________. [Take $$\varepsilon $$₀ = 8.85 $$\times$$ 10^$$-$$12 F/m]

Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is :

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s² and 4 m/s² respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.