The specific heat of water $=4200\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ ${}^{}{}^{}$ and the latent heat of ice $=3.4*{10}^5\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}$ ${}^{}{}^{}$ . 100 grams of ice at $0^{?}\mathrm{C}$ ${}^{}$ is placed in $200\mathrm{g}$ $$ of water at ${25}^{?}\mathrm{C}$ ${}^{}$ . The amount of ice that will melt as the temperature of water reaches $0^{?}\mathrm{C}$ ${}^{}$ is close to (in grams):

Two moles of helium gas are taken over the cycle ABCDA as shown below in P-T diagram. Assuming the gas to be ideal, the work done on the gas in taking from A to B is

Heat is supplied to an ideal monoatomic gas at constant pressure. The ratio of

An ideal engine whose efficiency is 40%, receives heat at 500 K. If required efficiency is 50%, then intake temperature for the same exhaust temperature is

Choose the correct statement.

Two waves of wavelength 50 cm and 51 cm produced 12 beats per second. The velocity of sound is