$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \ cal/sec$. If all the linear dimensions are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

Two sheets of thickness $d$ and $2d$ and the same area are touching each other on their faces. The temperatures $T_A$,$T_B$,and $T_C$ shown are in a geometric progression with a common ratio $r = 2$. Then,the ratio of the thermal conductivity of the thinner sheet to the thicker sheet 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 $^{\circ}C$)

Three rods made of the same material and having the same cross-sectional area but different lengths $10 \ cm$,$20 \ cm$,and $30 \ cm$ are joined as shown. The temperature of the joint is ....... $^oC$.

In a steady state, the graph between temperature $(\theta)$ and distance $(x)$ from the hot end is:

Three rods made of the same material and having the same cross-sectional area but different lengths $10\, cm, 20\, cm$,and $30\, cm$ are joined as shown. The temperature of the junction is ......... $^oC$.