An ice cube of dimensions $60 \mathrm{cm}\times 50 \mathrm{cm}\times 20 \mathrm{cm}$ is placed in an insulation box of wall thickness $1 \mathrm{cm}$. The box keeping the ice cube at $0°\mathrm{C}$ of temperature is brought to a room of temperature $40°\mathrm{C}$. The rate of melting of ice is approximately: (Latent heat of fusion of ice is $3.4\times {10}^5 \mathrm{J}{ \mathrm{kg}}^{-1}$ and thermal conduction of insulation wall is $0.05 \mathrm{W} {\mathrm{m}}^{-1} °{\mathrm{C}}^{-1}$)

If $K_1$ and $K_2$ are the thermal conductivities $L_1$ and $L_2$ are the lengths and $A_1$ and $A_2$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_2}{K_1}=9,\frac{A_1}{A_2}=2,\frac{L_1}{L_2}=2$. Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be

The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between upper fixed point and lower fixed point there are $150$ equal divisions of scale $P$ and $100$ divisions on scale $Q$. The relationship for conversion between the two scales is given by :

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Heat energy of $184 \mathrm{kJ}$ is given to ice of mass $600 \mathrm{g}$ at $-12 °\mathrm{C}$, Specific heat of ice is $2222.3 \mathrm{J} {\mathrm{kg}}^{–1} °{\mathrm{C}}^{–1}$, and the latent heat of ice is $336 \mathrm{kJ} {\mathrm{kg}}^{–1}$. Consider the statements below.

(A) Final temperature of the system will be $0 °\mathrm{C}$

(B) Final temperature of the system will be greater than $0 °\mathrm{C}$

(C) The final system will have a mixture of ice and water in the ratio of  $5 : 1$

(D) The final system will have a mixture of ice and water in the ratio of  $1 : 5$

(E) The final system will have water only

Choose the correct answer from the options given below :