Heat current is maximum in which of the following (rods are of identical dimension)?

Two rectangular blocks $A$ and $B$ of different metals have the same length and the same area of cross-section. They are kept in such a way that their cross-sectional areas touch each other. The temperature at one end of $A$ is $100^{\circ}C$ and that of $B$ at the other end is $0^{\circ}C$. If the ratio of their thermal conductivities is $1 : 3$,then under steady state,the temperature of the junction in contact will be ........ $^{\circ}C$.

Two rods $A$ and $B$ of the same cross-sectional area $A$ and length $l$ are connected in series between a source $(T_1 = 100^{\circ}C)$ and a sink $(T_2 = 0^{\circ}C)$ as shown in the figure. The rods are laterally insulated. If $G_A$ and $G_B$ are the temperature gradients across rod $A$ (thermal conductivity $3K$) and rod $B$ (thermal conductivity $K$),then:

Which of the following material properties is most suitable for a cooking utensil?

Three rods of the same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown in the figure with their ends at $100\,^{\circ}C, 50\,^{\circ}C$ and $20\,^{\circ}C$. The temperature of their junction is....... $^{\circ}C$

In a steady state,the temperatures at the ends $A$ and $B$ of a $20\,cm$ long rod $AB$ are $100\,^{\circ}C$ and $0\,^{\circ}C$ respectively. The temperature of a point $C$ at a distance of $9\,cm$ from $A$ is....... $^{\circ}C$