In variable state, the rate of flow of heat is controlled by

Three rods $A, B$ and $C$ of thermal conductivities $K, 2\,K$ and $4\,K$, cross-sectional  areas $A, 2\,A$ and $2\,A$ and lengths $2l, l$ and $l$ respectively are connected as shown  in the figure. If the ends of the rods are maintained at temperatures $100^o\,C, 50^o\,C$, and $0^o\,C$ respectively, then the temperature $\theta$ of the junction is ......... $^oC$

There is formation of layer of snow $x\,cm$ thick on water, when the temperature of air is $ - {\theta ^o}C$ (less than freezing point). The thickness of layer increases from $x$ to $y$ in the time $t$, then the value of $t$is given by

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.)

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

The two opposite faces of a cubical piece of iron (thermal conductivity $= 0.2\, CGS$ units) are at ${100^o}C$ and ${0^o}C$ in ice. If the area of a surface is $4c{m^2}$, then the mass of ice melted in $10$ minutes will be ...... $gm$