n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

A $$ \to $$ B : Isothermal expansion at temperature T so that the volume is doubled from V₁ to V₂ = 2V₁ and pressure charges from P₁ to P₂

B $$ \to $$ C : Isobaric compression at pressure P₂ to initial volume V₁.

C $$ \to $$ A : Isochoric change leading to change of pressure from P₂ to P₁.

Total workdone in the complete cycle ABCA is :

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '$$\alpha$$'. The metal sheet is heated uniformly, by a small temperature $$\Delta$$T, so that its new temperature is T + $$\Delta$$T. Calculate the increase in the volume of the metal box.

A cell E₁ of emf 6V and internal resistance 2$$\Omega$$ is connected with another cell E₂ of emf 4V and internal resistance 8$$\Omega$$ (as shown in the figure). The potential difference across points X and Y is :

The focal length f is related to the radius of curvature r of the spherical convex mirror by :