Which neighbouring country is located to the east of India?

Let $f\left(x\right)$ be a polynomial of degree four and having its extreme values at $x=1$ and $x=2$. If $\underset{x\to 0 }{\lim }\left[1+\frac{\mathrm{f}\left(x\right)}{x^2}\right]=3$, then $f\left(2\right)$ is equal to 

One mole of an ideal gas at $300 \mathrm{K}$ is expanded isothermally from an initial volume of $1$ litre to $10$ litre. $∆\mathrm{U}$ for this process is: 

$\left(\mathrm{R}=2\mathrm{ }\mathrm{cal}\mathrm{ }{\mathrm{mol}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}\right)$

The pressure (P) and density $\left(\rho \right)$ of a diatomic gas $\left(\gamma =\frac{7}{5}\right)$ changes from $P_1 ,{\rho }_1$ to $P_2,{\rho }_2$ . What is the value of $\frac{P_1}{P_2}$ if $\frac{{\rho }_1}{{\rho }_2}=32 ?$