Two identical conducting rods are first connected independently to two vessels, one containing water at $100°\mathrm{C}$ and the other containing ice at $0°\mathrm{C}$. In the second case, the rods are joined end to end and connected to the same vessels. Let $q_1$ and $q_2 \mathrm{g} {\mathrm{s}}^{-1}$ be the rate of melting of ice in two cases, respectively. The ratio of $\frac{q_1}{q_2}$ is

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0°\mathrm{C}$ and $90°\mathrm{C}$ respectively. The temperature of the junction of the three rods will be:

Three identical thermal conductors are connected as shown in figure. Consider no heat lost due to radiation, the temperature of the junction is