Heat energy of $184\,kJ$ is given to ice of mass $600\,g$ at $-12^{\circ}\,C$, Specific heat of ice is $2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}$ and latent heat of ice in $336\,kJ / kg ^{-1}$

$(A)$ Final temperature of system will be $0^{\circ} C$.

$(B)$ Final temperature of the system will be greater than $0^{\circ} C$.

$(C)$ 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:

The temperature of $100 \,gm$ of water is to be raised from $24^{\circ} C$ to $90^{\circ} C$ by adding steam to it. The mass of the steam required for this purpose is ........... $g$

$10\,gm$ of ice at $0\,^oC$ is mixed with $'m'\,gm$ of water at $50\,^oC$ . ........ $gm$ is minimum value of $m$ so that ice melts completely. ( $L_f = 80\,cal/gm$ and $S_W = 1\,cal/gm-\,^oC$ )

Steam at $100^o C$ is added slowly to $1400 \,\,gm$ of water at $16^o C$ until the temperature of water is raised to $80^o C$. The mass of steam required to do this is ($L_V =$  $540\,\,cal/gm$) ........... $gm$

Two identical blocks of metal are at $20^{\circ} C$ and $80^{\circ} C$, respectively. The specific heat of the material of the two blocks increases with temperature. Which of the following is true about the final temperature $T_f$ when the two blocks are brought into contact (assuming that no heat is lost to the surroundings)?

A refrigerator converts $500\,g$ of water at $25\,^oC$ into ice at $-10\,^oC$ in $3\,hours\,40\,minutes$ . The quantity of heat removed per minute is  ........ $cal/\min$

(Sp. heat of water $1\,cal/gm$, Specific heat of ice $= 0.5\,cal/g\,^oC$ , letent heat of fusion $= 80\,cal/g$ )