The number of integral terms in the expansion of $$\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}$$ is equal to ___________.

Given below are two statements :

Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statements II : $$\mathrm{Au} < \mathrm{Parsec} (\mathrm{Pc}) < \mathrm{ly}$$

In the light of the above statements, choose the most appropriate answer from the options given below:

$$1 \mathrm{~kg}$$ of water at $$100^{\circ} \mathrm{C}$$ is converted into steam at $$100^{\circ} \mathrm{C}$$ by boiling at atmospheric pressure. The volume of water changes from $$1.00 \times 10^{-3} \mathrm{~m}^{3}$$ as a liquid to $$1.671 \mathrm{~m}^{3}$$ as steam. The change in internal energy of the system during the process will be

(Given latent heat of vaporisaiton $$=2257 \mathrm{~kJ} / \mathrm{kg}$$, Atmospheric pressure = $$\left.1 \times 10^{5} \mathrm{~Pa}\right)$$

The critical angle for a denser-rarer interface is $$45^{\circ}$$. The speed of light in rarer medium is $$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$$. The speed of light in the denser medium is: