Three conducting rods of the same material and cross-section are shown in the figure. The temperatures of $A$,$D$,and $C$ are maintained at $20^{\circ} C$,$90^{\circ} C$,and $0^{\circ} C$ respectively. If there is no heat flow in rod $AB$,the ratio of the lengths of $BD$ and $BC$ is:

Two identical rods $AC$ and $CB$ made of two different metals having thermal conductivities in the ratio $2:3$ are kept in contact with each other at the end $C$. $A$ is at $100^{\circ}C$ and $B$ is at $25^{\circ}C$. Then the junction $C$ is at: (in $^{\circ}C$)

Four rods of the same material with different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct the most heat?

The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the interface is ........... $^{\circ} C$ (Thermal conductivity of iron and brass are $0.2$ and $0.3$ respectively.)

$A$ metal cooking pot has a base area of $0.2 \,m^2$ and a thickness of $2.0 \,cm$. It boils water at a rate of $3.0 \,kg/min$ when placed on a hot plate. What is the temperature of the part of the hot plate in contact with the pot (in $^{\circ} C$)? [Thermal conductivity of metal is $120 \,J s^{-1} m^{-1} K^{-1}$,latent heat of vaporisation of water is $2 \times 10^6 \,J/kg$]

$A$ cylindrical rod has temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is $Q \ J s^{-1}$. All the linear dimensions of the rod are doubled while keeping the temperatures constant. What is the new rate of flow of heat?