$A$ large box is connected to an ice cube at $100^{\circ}C$ by two identical metal rods as shown in the figure. The ice melts at a rate of $Q_1 \, g/s$. When the rods are connected in series between the box and the ice cube,the new melting rate is $Q_2 \, g/s$. Then $Q_2/Q_1$ is:

$A$ composite block is made of slabs $A, B, C, D$ and $E$ of different thermal conductivities (given in terms of a constant $K$) and sizes (given in terms of length,$L$) as shown in the figure. All slabs are of same width. Heat $Q$ flows only from left to right through the blocks. Then in steady state:
$(A)$ Heat flow through $A$ and $E$ slabs are same.
$(B)$ Heat flow through slab $E$ is maximum.
$(C)$ Temperature difference across slab $E$ is smallest.
$(D)$ Heat flow through $C =$ Heat flow through $B +$ Heat flow through $D$.

Two rods of same length and material transfer a given amount of heat in $12 \, s$ when they are joined end to end. But when they are joined lengthwise (parallel),they will transfer the same amount of heat under the same conditions in .......... $s$.

Two metal plates of equal thickness have thermal conductivities $K_1$ and $K_2$ respectively. They are joined together to form a single plate. The equivalent thermal conductivity of this composite plate is ..........

In a composite rod,two rods of different lengths and the same cross-sectional area are joined end to end. If $K$ is the equivalent coefficient of thermal conductivity of the composite rod,then $\left( \frac{\ell_1 + \ell_2}{K} \right)$ is equal to:

Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of thermal conductivity of each plate are $2$ and $3$ respectively,then the thermal conductivity of the composite plate will be: