Two rods of same length and material transfer a given amount of heat in $12 \ s$,when they are joined end to end. But when they are joined along their lengths (parallel combination),then they will transfer the same amount of heat under the same conditions in time $t = \dots \ s$.

$ABCDE$ is a regular pentagon made of uniform wire. Heat enters at $A$ and leaves at $C$. $T_B$ and $T_D$ are the temperatures of points $B$ and $D$ respectively. Find the temperature $T_C$.

Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends of these rods are maintained as indicated. Assuming no heat energy loss occurs through the curved surfaces of the rods,the temperature at the junction $X$ is (in $^{\circ} C$)

$A$ square is formed by four identical rods. If the temperature difference across one diagonal is $100^{\circ}C$,what will be the temperature difference across the other diagonal?

Two rods of cross-sectional area $A$ and $2A$ and equal length having thermal conductivities $2K$ and $3K$ are joined in parallel. The equivalent thermal conductivity of their combination will be:

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in the figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ}C$ and $40^{\circ}C$ respectively. Given the thermal conductivity of rod $x$ is three times that of rod $y$, the temperatures at junction points $B$ and $E$ are (close to):