hree rods of same dimensions are arranged as shown in figure they have thermal conductivities ${K_1},{K_2}$ and${K_3}$ The points $P$ and $Q$ are maintained at different temperatures for the heat to flow at the same rate along $PRQ$ and $PQ$ then which of the following option is correct

Two rectangular blocks, having identical dimensions, can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x-$ axis is the same in both the configurations. It takes $9s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is .......... $\sec$

Four rods of same material and having the same cross section and length have been joined, as shown. The temperature of junction of four rods will be........ $^oC$

As per the given figure, two plates $A$ and $B$ of thermal conductivity $K$ and $2 K$ are joined together to form a compound plate. The thickness of plates are $4.0 \,cm$ and $2.5 \,cm$ respectively and the area of cross-section is $120 \,cm ^{2}$ for each plate. The equivalent thermal conductivity of the compound plate is $\left(1+\frac{5}{\alpha}\right) K$, then the value of $\alpha$ will be_______

In a steady state, the temperature at the end $A$ and $B$ of $20\,cm$ long rod $AB$ are $100\,^oC$ and $0\,^oC$ respectively. The temperature of a point $9\,cm$ from $A$ is....... $^oC$

In the Ingen Hauz’s experiment the wax melts up to lengths $10$ and $25 cm$ on two identical rods of different materials. The ratio of thermal conductivities of the two materials is