Two conducting rods $A$ and $B$ of same length and cross-sectional area are connected $(i)$ In series $(ii)$ In parallel as shown. In both combination a temperature difference of $100^o C$ is maintained. If thermal conductivity of $A$ is $3K$ and that of $B$ is $K$ then the ratio of heat current flowing in parallel combination to that flowing in series combination is

Which of the following circular rods. (given radius $ r$ and length $l$ ) each made of the same material as whose ends are maintained at the same temperature will conduct most heat

If two metallic plates of equal thicknesses and thermal conductivities ${K_1}$ and ${K_2}$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

Ice starts forming in lake with water at ${0^o}C$ and when the atmospheric temperature is $ - {10^o}C$. If the time taken for $1 \;cm$ of ice be $7$ hours, then the time taken for the thickness of ice to change from $1\; cm$ to $2\; cm$ is

Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $385\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ and $50\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\,C$ and $0^{\circ}\,C$ respectively. The temperature at the junction is, nearly $.......^{\circ}\,C$

In the following figure, two insulating sheets with thermal resistances $R$ and $3R$ as shown in figure. The temperature $\theta$ is ...... $^oC$