Two rods of the same length and material transfer a given amount of heat in $12 \text{ s}$ when they are joined end-to-end. If they are joined lengthwise, in how many seconds will they transfer the same amount of heat under the same conditions (in $\text{ s}$)?

Three rods $AB, BC$ and $AC$ having thermal resistances of $10 \text{ units}, 10 \text{ units}$ and $20 \text{ units}$ respectively,are connected as shown in the figure. Ends $A$ and $C$ are maintained at constant temperatures of $100^{\circ}C$ and $0^{\circ}C$ respectively. The rate at which the heat is crossing junction $B$ is . . . . . . $units$.

Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} C$, while the second surface of slab $B$ is maintained at $25^{\circ} C$. The temperature at the contact of their surfaces is (in $^{\circ} C$)

Two identical conducting rods are first connected independently to two vessels,one containing water at $100^{\circ}C$ and the other containing ice at $0^{\circ}C$. In the second case,the rods are joined end to end and connected to the same vessels. Let $q_1$ and $q_2$ $g/s$ be the rate of melting of ice in the two cases respectively. The ratio $q_2/q_1$ is

Six identical conducting rods are joined as shown. The ends $A$ and $D$ are maintained at $200\,^{\circ}C$ and $20\,^{\circ}C$ respectively. No heat is lost to the surroundings. The temperature of the junction $C$ will be ........ $^{\circ}C$.

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?