The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

A source supplies heat to a system at the rate of $$1000 \mathrm{~W}$$. If the system performs work at a rate of $$200 \mathrm{~W}$$. The rate at which internal energy of the system increases is

The number of air molecules per cm$$^3$$ increased from $$3\times10^{19}$$ to $$12\times10^{19}$$. The ratio of collision frequency of air molecules before and after the increase in number respectively is:

A Carnot engine operating between two reservoirs has efficiency $$\frac{1}{3}$$. When the temperature of cold reservoir raised by x, its efficiency decreases to $$\frac{1}{6}$$. The value of x, if the temperature of hot reservoir is $$99^\circ$$C, will be :