$1\,\, kg$ of ice at $-10^o C$ is mixed with $4.4\,\, kg$ of water at $30^o C$. The final temperature of mixture is ........$^oC$ (specific heat of ice is $2100\,\,J/kg/k$)

Pure water super cooled to $-15^o C$ is contained in a thermally insulated flask. Small amount of ice is thrown into the flask. The fraction of water frozen into ice is :

$10\, gm$ of ice at $-20°C$ is dropped into a calorimeter containing $10\, gm$ of water at $10°C;$ the specific heat of water is twice that of ice. When equilibrium is reached, the calorimeter will contain

A liquid of mass $M$ and specific heat $S$ is at a temperature $2t$. If another liquid of thermal capacity $1.5$ times, at a temperature of $\frac{t}{3}$ is added to it, the resultant temperature will be

A metal bal of mass $0.1\, kg$ is heated upto $500\,{}^oC$ and dropped into a vessel of heat capacity $800\, JK^{-1}$ and containing $0.5\, kg$ water. The initial temperature of water and vessel is $30\,{}^oC$. ........ $\%$ is the approximate percentage increment in the temperature of the water. [Specific heat Capacities of water and metal are, respectively $4200\, Jkg^{-1}K^{-1}$ and $400\, Jkg^{-1}K^{-1}$]

A piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $h$ is

[Latent heat of ice is $3.4 \times 10^{5}\; J / k g$ and $g=10\; N / kg ]$