Two containers have the same shape and wall thickness but are made of different materials. They are filled with the same amount of ice at $0^{\circ}C$. If the ice melts completely in $10$ minutes and $25$ minutes respectively,what is the ratio of the thermal conductivities of the materials of the containers?

$A$ copper rod and a steel rod of equal cross-sections and lengths $L$ are joined side by side and connected between two heat baths as shown in the figure. If heat flows through them from $x = 0$ to $x = 2L$ at a steady rate and thermal conductivities of the metals are $K_{Cu}$ and $K_{Steel}$ $(K_{Cu} > K_{Steel})$,then the temperature varies as (convection and radiation are negligible):

$A$ rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio $4: 1$. If the free face of brass is at $0^{\circ} C$ and that of copper is at $100^{\circ} C$,then the temperature of their interface is (in $^{\circ} C$)

$A$ composite slab is prepared with two different materials $A$ and $B$. The relation between their coefficients of thermal conductivity and thickness is given as $K_A = \frac{K_B}{2}$ and $X_A = 2 X_B$, respectively. If the temperatures of the outer faces of $A$ and $B$ are $75^{\circ} C$ and $50^{\circ} C$ respectively, what will be the temperature of the common surface (in $^{\circ} C$)?

The end $A$ of a rod $AB$ of length $1\,m$ is maintained at $80\,^{\circ}C$ and the end $B$ at $0\,^{\circ}C$. The temperature at a distance of $60\,cm$ from the end $A$ is......... $^{\circ}C$

Which of the following material properties is most suitable for a cooking utensil?