The ratio of thermal conductivity of two rods $A$ and $B$ with the same area of cross-section is $3: 2$. If the thermal resistance of two rods is the same,then the ratio of length of rod $A$ to length of rod $B$ is

Three identical rods $A, B$ and $C$ are placed end to end. $A$ temperature difference is maintained between the free ends of $A$ and $C$. The thermal conductivity of $B$ is thrice that of $C$ and half of that of $A$. The effective thermal conductivity of the system will be ($K_{A}$ is the thermal conductivity of rod $A$).

Two rods of equal length and diameter have thermal conductivities $3$ and $4$ units respectively. If they are joined in series,the thermal conductivity of the combination would be

$A$ metallic prong consists of $4$ rods made of the same material,with the same cross-sections and the same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$.

$A$ composite slab consists of two materials having coefficients of thermal conductivity $K$ and $2K$,thickness $x$ and $4x$ respectively. The temperatures of two outer surfaces of the composite slab are $T_2$ and $T_1$ respectively $(T_2 > T_1)$. The rate of heat transfer through the slab in a steady state is $\left[\frac{A(T_2 - T_1)K}{x}\right] f$,where $f$ is equal to:

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 ........ $^{\circ}C$.