$A$ block of ice at $-20\,^oC$ having a mass of $2\, kg$ is added to $3\, kg$ of water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container,which of the following is true?

$Assertion :$ In the pressure-temperature $(P-T)$ phase diagram of water,the slope of the melting curve is found to be negative.
$Reason :$ Ice contracts on melting to water.

The variation of density of water with temperature is represented by the

Calculate the heat required to convert $3 \; kg$ of ice at $-12 \; ^{\circ}C$ kept in a calorimeter to steam at $100 \; ^{\circ}C$ at atmospheric pressure. Given: specific heat capacity of ice $= 2100 \; J \; kg^{-1} \; K^{-1}$,specific heat capacity of water $= 4186 \; J \; kg^{-1} \; K^{-1}$,latent heat of fusion of ice $= 3.35 \times 10^{5} \; J \; kg^{-1}$,and latent heat of steam $= 2.256 \times 10^{6} \; J \; kg^{-1}$.

The temperature of a body is given by $T = 6t^2 + 4$. The rate of change of temperature with respect to time at $t = 10 \ s$ is ........ $K/s$. ($T$ is in $Kelvin$ and $t$ is in $seconds$)

$A$ lead bullet at $27\ ^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle,the velocity of the bullet at the time of striking is ....... $m/s$. (Melting point of lead $= 327\ ^oC$,specific heat of lead $= 0.03\ cal/g\ ^oC$,latent heat of fusion of lead $= 6\ cal/g$,and $J = 4.2\ J/cal$)