One mole of a diatomic ideal gas undergoes a cyclic process $$ABC$$ as shown in figure. The process $$BC$$ is adiabatic. The temperatures at $$A, B$$ and $$C$$ are $$400$$ $$K$$, $$800$$ $$K$$ and $$600$$ $$K$$ respectively. Choose the correct statement :

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are filled in the tube. Each liquid subtends $${90^ \circ }$$ angle at center. Radius joining their interface makes an angle $$\alpha $$ with vertical. Radio $${{{d_1}} \over {{d_2}}}$$ is :

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $$R$$ and making a circular contact of radius $$r$$ with the bottom $$R$$ and making a circular contact of radius $$r$$ with the bottom of the vessel. If $$r < < R$$ and the surface tension of water is $$T,$$ value of $$r$$ just before bubbles detach is: (density of water is $${\rho _w}$$)

Three rods of Copper, Brass and Steel are welded together to form a $$Y$$ shaped structure. Area of cross - section of each rod $$ = 4c{m^2}.$$ End of copper rod is maintained at $${100^ \circ }C$$ where as ends of brass and steel are kept at $${0^ \circ }C$$. Lengths of the copper, brass and steel rods are $$46,$$ $$13$$ and $$12$$ $$cms$$ respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are $$0.92, 0.26$$ and $$0.12$$ $$CGS$$ units respectively. Rate of heat flow through copper rod is: