Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of thermal conductivity of each plate are $2$ and $3$ respectively,then the thermal conductivity of the composite plate will be:

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

An insulated container is filled with ice at $0\,^{\circ}\text{C}$,and another container is filled with water that is continuously boiling at $100\,^{\circ}\text{C}$. In a series of experiments,the containers are connected by various thick metal rods that pass through the walls of the container as shown in the figure.
In experiment $I$: a copper rod is used and all ice melts in $20$ minutes.
In experiment $II$: a steel rod of identical dimensions is used and all ice melts in $80$ minutes.
In experiment $III$: both the rods are used in series and all ice melts in $t_{10}$ minutes.
In experiment $IV$: both rods are used in parallel and all ice melts in $t_{20}$ minutes.

The ratio of the coefficient of thermal conductivity of two different materials is $5 : 3$. If the thermal resistance of the rods and the cross-sectional area of these materials are the same,then the ratio of the lengths of these rods will be

Two metal rods are arranged as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. What is their equivalent thermal conductivity?

Five identical rods are joined as shown in the figure. Points $A$ and $C$ are maintained at temperatures $120^\circ C$ and $20^\circ C$ respectively. The temperature of junction $B$ will be....... $^\circ C$