CH$_3$–Br $\xrightarrow{\text{CH$_3$OH/Nu}}$ CH$_3$OH
Correct order of rate of this reaction for given nucleophile:
Step 1: Understanding nucleophilicity.
Nucleophilicity refers to the ability of a nucleophile to donate electrons to form a new bond with an electrophile (in this case, CH$_3$–Br). The stronger the nucleophile, the faster the nucleophilic substitution reaction will occur.
Step 2: Comparing the nucleophilicity of the given nucleophiles.
- I$^-$ is the most nucleophilic due to its larger size and lower electronegativity, which makes it more willing to donate electrons.
- C$_2$H$_5$O$^-$ (ethoxide) is a good nucleophile, but not as strong as I$^-$, because oxygen is more electronegative, making it less willing to donate electrons.
- PhO$^-$ (phenoxide) is also a strong nucleophile, but the resonance stabilization of the phenoxide ion reduces its nucleophilicity compared to C$_2$H$_5$O$^-$ and I$^-$.
- F$^-$ is the least nucleophilic because fluorine is highly electronegative, making it reluctant to donate electrons.
Step 3: Conclusion.
The correct order of nucleophilicity is I$^-$>C$_2$H$_5$O$^-$>PhO$^-$>F$^-$, which corresponds to option (3).

Match the LIST-I with LIST-II: 
Choose the correct answer from the options given below:
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]