Three identical rods have been joined at a junction to make a $Y$-shaped structure. If two free ends are maintained at $90\,^{\circ}C$ and the third end is at $30\,^{\circ}C$,what is the junction temperature $\theta$ in $^{\circ}C$?

The ratio of thermal conductivities of two materials is $1 : 2$. If the ratio of the lengths of the rods of these materials is $1 : 2$ and the ratio of their cross-sectional areas is $2 : 1$,then the ratio of their thermal resistances is:

Four rods of the same material and having the same cross-section and length have been joined as shown in the figure. The temperature of the junction of the four rods will be ............... $^{\circ}C$.

Three rods $AB$,$BC$,and $BD$ made of the same material and having the same cross-section have been joined as shown in the figure. The ends $A$,$C$,and $D$ are held at temperatures of $20^{\circ} C$,$80^{\circ} C$,and $80^{\circ} C$ respectively. If each rod is of the same length,then the temperature at the junction $B$ of the three rods is: (in $^{\circ} C$)

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

Three rods of the same material,same length,and same cross-sectional area are connected as shown in the figure. Find the temperature of their junction in $^oC$.