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:


Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).

Match the LIST-I with LIST-II for an isothermal process of an ideal gas system. 
Choose the correct answer from the options given below:
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?
